C₅×#73006 #14510730

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

solvable

Aliases

direct product

C₅×#73006

Splittings

Fitting

C₅×#399 ⋊ D₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅	#857⋊C₂
commutator, cosocle, hypocenter	#95⋊C₃	C₂²×C₅
Frattini	C₂³	C₂×C₅×S₄
Fitting	C₅×#399	D₃
socle	C₂³×C₅	C₂×S₄
LCS	G ▷ #95⋊C₃
UCS	C₁ ◁ C₂×C₅

228 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 24 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) = 240

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

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

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236428);