#72239931

order	3840
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle, hypercenter	C₂	#14515297
commutator, prime radical, hypocenter	#14515301	C₂
Frattini, cosocle	C₂⁵	C₂×A₅
Fitting	C₂⁴×C₄	A₅
LCS	G ▷ #14515301
UCS	C₁ ◁ C₂

325 conjugacy classes of subgroups; only the 6 normal subgroups are shown.

normal subgroups only

This group has 325 conjugacy classes of subgroups — too many to draw. Only its 6 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 48 points:

(1,6,5,19)(2,11,10,31)(3,15,14,38)(4,18,17,42)(7,20,23,40)(8,27,26,46)(9,30,29,33)(12,35,28,47)(13,37,36,41)(16,21,22,43)(24,32,34,48)(25,45,44,39);(2,36,8,7,25)(3,12,4,34,29)(6,35,31,41,48)(9,14,28,17,24)(10,13,26,23,44)(11,37,32,19,47)(15,39,21,46,30)(27,33,38,45,43)

Conjugacy classes & character table

26 conjugacy classes — view the full character table.

Relationships

maximal subgroup of

#72239932

GAP

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

gap> G := Group((1,6,5,19)(2,11,10,31)(3,15,14,38)(4,18,17,42)(7,20,23,40)(8,27,26,46)(9,30,29,33)(12,35,28,47)(13,37,36,41)(16,21,22,43)(24,32,34,48)(25,45,44,39), (2,36,8,7,25)(3,12,4,34,29)(6,35,31,41,48)(9,14,28,17,24)(10,13,26,23,44)(11,37,32,19,47)(15,39,21,46,30)(27,33,38,45,43));