C₅×#72988 #14510712

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

solvable

Aliases

direct product

C₅×#72988

Splittings

Fitting

C₅×#376 ⋊ D₃

Subgroups

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

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

normal subgroups only

This group has 260 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) = 29
transitive degree	μ_t(G) = 120

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

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236410);