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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{100}=b^{101}=1, b^{a}=b^{28} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P 101P
$F_{101}$ 1A $1$ $1$ $F_{101}$ 1A 1A 1A $1$
$F_{101}$ 2A $2$ $101$ $C_{100}$ 1A 2A 2A $a^{50}b^{92}$
$F_{101}$ 4A1 $4$ $101$ $C_{100}$ 2A 4A1 4A1 $a^{75}b^{91}$
$F_{101}$ 4A-1 $4$ $101$ $C_{100}$ 2A 4A-1 4A-1 $a^{25}b$
$F_{101}$ 5A1 $5$ $101$ $C_{100}$ 5A2 1A 5A1 $a^{20}b^{19}$
$F_{101}$ 5A-1 $5$ $101$ $C_{100}$ 5A-2 1A 5A-1 $a^{80}b^{20}$
$F_{101}$ 5A2 $5$ $101$ $C_{100}$ 5A-1 1A 5A2 $a^{40}b^{6}$
$F_{101}$ 5A-2 $5$ $101$ $C_{100}$ 5A1 1A 5A-2 $a^{60}b^{84}$
$F_{101}$ 10A1 $10$ $101$ $C_{100}$ 5A1 2A 10A1 $a^{10}b^{8}$
$F_{101}$ 10A-1 $10$ $101$ $C_{100}$ 5A-1 2A 10A-1 $a^{90}b^{86}$
$F_{101}$ 10A3 $10$ $101$ $C_{100}$ 5A-2 2A 10A3 $a^{30}b^{72}$
$F_{101}$ 10A-3 $10$ $101$ $C_{100}$ 5A2 2A 10A-3 $a^{70}b^{73}$
$F_{101}$ 20A1 $20$ $101$ $C_{100}$ 10A1 4A1 20A1 $a^{55}b^{89}$
$F_{101}$ 20A-1 $20$ $101$ $C_{100}$ 10A-1 4A-1 20A-1 $a^{45}b^{13}$
$F_{101}$ 20A3 $20$ $101$ $C_{100}$ 10A3 4A-1 20A3 $a^{65}b^{42}$
$F_{101}$ 20A-3 $20$ $101$ $C_{100}$ 10A-3 4A1 20A-3 $a^{35}b^{22}$
$F_{101}$ 20A7 $20$ $101$ $C_{100}$ 10A-3 4A-1 20A7 $a^{85}b^{70}$
$F_{101}$ 20A-7 $20$ $101$ $C_{100}$ 10A3 4A1 20A-7 $a^{15}b^{50}$
$F_{101}$ 20A9 $20$ $101$ $C_{100}$ 10A-1 4A1 20A9 $a^{95}b^{79}$
$F_{101}$ 20A-9 $20$ $101$ $C_{100}$ 10A1 4A-1 20A-9 $a^{5}b^{3}$
$F_{101}$ 25A1 $25$ $101$ $C_{100}$ 25A2 5A1 25A1 $a^{4}b^{12}$
$F_{101}$ 25A-1 $25$ $101$ $C_{100}$ 25A-2 5A-1 25A-1 $a^{96}b^{61}$
$F_{101}$ 25A2 $25$ $101$ $C_{100}$ 25A4 5A2 25A2 $a^{8}b^{56}$
$F_{101}$ 25A-2 $25$ $101$ $C_{100}$ 25A-4 5A-2 25A-2 $a^{92}b^{96}$
$F_{101}$ 25A3 $25$ $101$ $C_{100}$ 25A6 5A-2 25A3 $a^{12}b^{49}$
$F_{101}$ 25A-3 $25$ $101$ $C_{100}$ 25A-6 5A2 25A-3 $a^{88}b^{78}$
$F_{101}$ 25A4 $25$ $101$ $C_{100}$ 25A8 5A-1 25A4 $a^{16}b^{57}$
$F_{101}$ 25A-4 $25$ $101$ $C_{100}$ 25A-8 5A1 25A-4 $a^{84}b^{18}$
$F_{101}$ 25A6 $25$ $101$ $C_{100}$ 25A12 5A1 25A6 $a^{24}b^{48}$
$F_{101}$ 25A-6 $25$ $101$ $C_{100}$ 25A-12 5A-1 25A-6 $a^{76}b^{94}$
$F_{101}$ 25A7 $25$ $101$ $C_{100}$ 25A-11 5A2 25A7 $a^{28}b^{87}$
$F_{101}$ 25A-7 $25$ $101$ $C_{100}$ 25A11 5A-2 25A-7 $a^{72}b^{4}$
$F_{101}$ 25A8 $25$ $101$ $C_{100}$ 25A-9 5A-2 25A8 $a^{32}b^{28}$
$F_{101}$ 25A-8 $25$ $101$ $C_{100}$ 25A9 5A2 25A-8 $a^{68}b^{7}$
$F_{101}$ 25A9 $25$ $101$ $C_{100}$ 25A-7 5A-1 25A9 $a^{36}b^{81}$
$F_{101}$ 25A-9 $25$ $101$ $C_{100}$ 25A7 5A1 25A-9 $a^{64}b^{17}$
$F_{101}$ 25A11 $25$ $101$ $C_{100}$ 25A-3 5A1 25A11 $a^{44}b^{34}$
$F_{101}$ 25A-11 $25$ $101$ $C_{100}$ 25A3 5A-1 25A-11 $a^{56}b^{38}$
$F_{101}$ 25A12 $25$ $101$ $C_{100}$ 25A-1 5A2 25A12 $a^{48}b^{2}$
$F_{101}$ 25A-12 $25$ $101$ $C_{100}$ 25A1 5A-2 25A-12 $a^{52}b^{53}$
$F_{101}$ 50A1 $50$ $101$ $C_{100}$ 25A1 10A1 50A1 $a^{2}b^{39}$
$F_{101}$ 50A-1 $50$ $101$ $C_{100}$ 25A-1 10A-1 50A-1 $a^{98}b^{90}$
$F_{101}$ 50A3 $50$ $101$ $C_{100}$ 25A3 10A3 50A3 $a^{6}b^{54}$
$F_{101}$ 50A-3 $50$ $101$ $C_{100}$ 25A-3 10A-3 50A-3 $a^{94}b^{58}$
$F_{101}$ 50A7 $50$ $101$ $C_{100}$ 25A7 10A-3 50A7 $a^{14}b^{75}$
$F_{101}$ 50A-7 $50$ $101$ $C_{100}$ 25A-7 10A3 50A-7 $a^{86}b^{11}$
$F_{101}$ 50A9 $50$ $101$ $C_{100}$ 25A9 10A-1 50A9 $a^{18}b^{85}$
$F_{101}$ 50A-9 $50$ $101$ $C_{100}$ 25A-9 10A1 50A-9 $a^{82}b^{64}$
$F_{101}$ 50A11 $50$ $101$ $C_{100}$ 25A11 10A1 50A11 $a^{22}b^{88}$
$F_{101}$ 50A-11 $50$ $101$ $C_{100}$ 25A-11 10A-1 50A-11 $a^{78}b^{5}$
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