Properties

Label 25T1
Order \(25\)
n \(25\)
Cyclic Yes
Abelian Yes
Solvable Yes
Primitive No
$p$-group Yes
Group: $C_{25}$

Related objects

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Group action invariants

Degree $n$ :  $25$
Transitive number $t$ :  $1$
Group :  $C_{25}$
Parity:  $1$
Primitive:  No
Nilpotency class:  $1$
Generators:  (1,10,14,16,25,4,8,12,19,23,2,6,15,17,21,5,9,13,20,24,3,7,11,18,22)
$|\Aut(F/K)|$:  $25$

Low degree resolvents

|G/N|Galois groups for stem field(s)
5:  $C_5$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 5: $C_5$

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

Cycle TypeSizeOrderRepresentative
$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1$ $1$ $()$
$ 5, 5, 5, 5, 5 $ $1$ $5$ $( 1, 2, 3, 4, 5)( 6, 7, 8, 9,10)(11,12,13,14,15)(16,17,18,19,20) (21,22,23,24,25)$
$ 5, 5, 5, 5, 5 $ $1$ $5$ $( 1, 3, 5, 2, 4)( 6, 8,10, 7, 9)(11,13,15,12,14)(16,18,20,17,19) (21,23,25,22,24)$
$ 5, 5, 5, 5, 5 $ $1$ $5$ $( 1, 4, 2, 5, 3)( 6, 9, 7,10, 8)(11,14,12,15,13)(16,19,17,20,18) (21,24,22,25,23)$
$ 5, 5, 5, 5, 5 $ $1$ $5$ $( 1, 5, 4, 3, 2)( 6,10, 9, 8, 7)(11,15,14,13,12)(16,20,19,18,17) (21,25,24,23,22)$
$ 25 $ $1$ $25$ $( 1, 6,11,19,24, 4, 9,14,17,22, 2, 7,12,20,25, 5,10,15,18,23, 3, 8,13,16,21)$
$ 25 $ $1$ $25$ $( 1, 7,13,17,23, 4,10,11,20,21, 2, 8,14,18,24, 5, 6,12,16,22, 3, 9,15,19,25)$
$ 25 $ $1$ $25$ $( 1, 8,15,20,22, 4, 6,13,18,25, 2, 9,11,16,23, 5, 7,14,19,21, 3,10,12,17,24)$
$ 25 $ $1$ $25$ $( 1, 9,12,18,21, 4, 7,15,16,24, 2,10,13,19,22, 5, 8,11,17,25, 3, 6,14,20,23)$
$ 25 $ $1$ $25$ $( 1,10,14,16,25, 4, 8,12,19,23, 2, 6,15,17,21, 5, 9,13,20,24, 3, 7,11,18,22)$
$ 25 $ $1$ $25$ $( 1,11,24, 9,17, 2,12,25,10,18, 3,13,21, 6,19, 4,14,22, 7,20, 5,15,23, 8,16)$
$ 25 $ $1$ $25$ $( 1,12,21, 7,16, 2,13,22, 8,17, 3,14,23, 9,18, 4,15,24,10,19, 5,11,25, 6,20)$
$ 25 $ $1$ $25$ $( 1,13,23,10,20, 2,14,24, 6,16, 3,15,25, 7,17, 4,11,21, 8,18, 5,12,22, 9,19)$
$ 25 $ $1$ $25$ $( 1,14,25, 8,19, 2,15,21, 9,20, 3,11,22,10,16, 4,12,23, 6,17, 5,13,24, 7,18)$
$ 25 $ $1$ $25$ $( 1,15,22, 6,18, 2,11,23, 7,19, 3,12,24, 8,20, 4,13,25, 9,16, 5,14,21,10,17)$
$ 25 $ $1$ $25$ $( 1,16, 8,23,15, 5,20, 7,22,14, 4,19, 6,21,13, 3,18,10,25,12, 2,17, 9,24,11)$
$ 25 $ $1$ $25$ $( 1,17,10,21,14, 5,16, 9,25,13, 4,20, 8,24,12, 3,19, 7,23,11, 2,18, 6,22,15)$
$ 25 $ $1$ $25$ $( 1,18, 7,24,13, 5,17, 6,23,12, 4,16,10,22,11, 3,20, 9,21,15, 2,19, 8,25,14)$
$ 25 $ $1$ $25$ $( 1,19, 9,22,12, 5,18, 8,21,11, 4,17, 7,25,15, 3,16, 6,24,14, 2,20,10,23,13)$
$ 25 $ $1$ $25$ $( 1,20, 6,25,11, 5,19,10,24,15, 4,18, 9,23,14, 3,17, 8,22,13, 2,16, 7,21,12)$
$ 25 $ $1$ $25$ $( 1,21,16,13, 8, 3,23,18,15,10, 5,25,20,12, 7, 2,22,17,14, 9, 4,24,19,11, 6)$
$ 25 $ $1$ $25$ $( 1,22,18,11, 7, 3,24,20,13, 9, 5,21,17,15, 6, 2,23,19,12, 8, 4,25,16,14,10)$
$ 25 $ $1$ $25$ $( 1,23,20,14, 6, 3,25,17,11, 8, 5,22,19,13,10, 2,24,16,15, 7, 4,21,18,12, 9)$
$ 25 $ $1$ $25$ $( 1,24,17,12,10, 3,21,19,14, 7, 5,23,16,11, 9, 2,25,18,13, 6, 4,22,20,15, 8)$
$ 25 $ $1$ $25$ $( 1,25,19,15, 9, 3,22,16,12, 6, 5,24,18,14, 8, 2,21,20,11,10, 4,23,17,13, 7)$

Group invariants

Order:  $25=5^{2}$
Cyclic:  Yes
Abelian:  Yes
Solvable:  Yes
GAP id:  [25, 1]
Character table: Data not available.