C₅×#73153 #14510877

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂²

solvable

Aliases

direct product

C₅×#73153

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	C₂×C₅×H(5,𝔽₂)	D₃
prime radical	C₂×C₅×#994	C₂
cosocle	C₂×#41⋊C₃	C₂²×C₅
hypercenter	C₂×C₅×Q₈	S₄
hypocenter	SL(2,𝔽₃)	C₅×C₂²⋊C₄
LCS	G ▷ #41⋊C₃ ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×Q₈

420 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 60 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)(10,28,33,15,20,30,16,23,26,11,22,29)(12,25,27,14,24,21,18,17,31,19,13,32);(6,7,8,9)(11,14)(12,18)(13,21)(15,19)(17,26)(20,29)(22,30)(23,27)(24,32)(25,33)(28,31)

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, 236575);