#72224461

order	15600
automorphism	Aut(G) = PΓL(2,𝔽₂₅) (order 31200) · Inn(G) = G · Out(G) = C₂
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, prime radical, cosocle, hypocenter	PSL(2,𝔽₂₅)	C₂
LCS	G ▷ PSL(2,𝔽₂₅)
UCS	C₁

39 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 26

A minimal faithful permutation representation — 2 generators on 26 points:

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

Conjugacy classes & character table

15 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	PΓL(2,𝔽₂₅)
maximal normal subgroup of	PΓL(2,𝔽₂₅)

GAP

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

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