C₅×#85552 #14511290

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, socle, hypercenter	C₂²×C₅	#1020
commutator, cosocle, hypocenter	Q₈⋊SL(2,𝔽₃)	C₂×C₅
Frattini	C₂²	C₅×#1020
Fitting	C₅×Q₈²	D₃
prime radical	C₅×Q₈⋊SL(2,𝔽₃)	C₂
LCS	G ▷ Q₈⋊SL(2,𝔽₃)
UCS	C₁ ◁ C₂²×C₅

186 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.

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

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 640

A minimal faithful permutation representation — 2 generators on 29 points:

(1,2,3,4,5)(6,12,11,8,9,7,13,10)(14,25,26,22,18,19,23,20)(15,16,29,17,21,24,28,27);(7,11,8)(10,12,13)(16,17,26)(19,20,29)(22,28,25)(23,24,27)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236988);