C₅×#67998 #14510657

order	1920
isoclinism	isoclinic class of #4625
automorphism	?
homology	Abelianization (H₁) = C₅×C₈ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅×#67998

Splittings

derived

C₂²⋊A₄ ⋊ C₅×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅	#4625
commutator, hypocenter	C₂²⋊A₄	C₅×C₈
Frattini	C₂²×C₄	C₅×S₄
Fitting	C₅×#379	D₃
socle	C₂³×C₅	SL(2,ℤ/4)
prime radical	C₂×C₅×C₂²⋊A₄	C₄
cosocle	#379⋊C₃	C₂×C₅
LCS	G ▷ C₂²⋊A₄
UCS	C₁ ◁ C₂×C₅

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

normal subgroups only

This group has 162 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) = 29
transitive degree	μ_t(G) = 120

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236355);