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C25×C9⋊C9 #72276010

order2592
nilpotency class2
automorphism?
homologyAbelianization (H1) = C25×C3×C9 · Schur multiplier (H2) = C210×C3

Aliases

direct productC25×C9⋊C9

Subgroups

subgroupG/H
center, socle, prime radicalC25×C32C32
commutatorC3C25×C3×C9
Frattini, cosocleC32C25×C32
LCSG ▷ C3 ▷ C1
UCSC1 ◁ C25×C32 ◁ G

6358 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 2592

A minimal faithful permutation representation — 5 generators on 28 points:

(1,2)(12,14,17)(15,19,18)(20,21,23,22,24,26,25,27,28);(3,4)(11,12,15,16,17,19,13,14,18);(5,6);(7,8);(9,10)

Conjugacy classes & character table

1056 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup ofC23×#11757417, C2×C22⋊A4×C9⋊C9, C2×#72229238, …
maximal subgroup ofC23×#11757417, C2×C22⋊A4×C9⋊C9, C2×#72229238
maximal normal subgroup ofC23×#11757417, C2×C22⋊A4×C9⋊C9, C2×#72229238

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2)(12,14,17)(15,19,18)(20,21,23,22,24,26,25,27,28), (3,4)(11,12,15,16,17,19,13,14,18), (5,6), (7,8), (9,10));