C₅×#73076 #14510800

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂

solvable

Aliases

direct product

C₅×#73076

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅	GL(2,ℤ/4)
commutator	#41⋊C₃	C₂×C₄×C₅
Frattini	C₂×C₄	C₂×C₅×S₄
Fitting	C₅×#520	D₃
prime radical	C₂×C₅×#41⋊C₃	C₂²
cosocle	C₂×#41⋊C₃	C₂²×C₅
hypercenter	C₅×C₄⋊C₄	S₄
hypocenter	SL(2,𝔽₃)	C₅×C₄⋊C₄
LCS	G ▷ #41⋊C₃ ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₅×C₄⋊C₄

280 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 33
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 2 generators on 33 points:

(1,2,3,4,5)(6,7,8,9)(10,30,33,16,21,27,12,25,31,11,24,32)(13,26,22,15,19,23,18,17,28,20,14,29);(10,11,13,15,12,16,18,20)(14,22,21,31,19,28,24,33)(17,27,25,29,26,32,30,23)

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236498);