C₅×#72987 #14510711

order	1920
isoclinism	isoclinic class of #4621
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

solvable

Aliases

direct product

C₅×#72987

Splittings

Fitting

C₅×#376 ⋊ D₃

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₅	#857
commutator, cosocle, hypocenter	#95⋊C₃	C₂²×C₅
Frattini	C₂³	C₂×C₅×S₄
Fitting	C₅×#376	D₃
socle	C₂³×C₅	C₂×S₄
prime radical	C₅×#4622	C₂
LCS	G ▷ #95⋊C₃
UCS	C₁ ◁ C₄×C₅

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

normal subgroups only

This group has 226 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.

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236409);