C₅×#72985 #14510709

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

solvable

Aliases

direct product

C₅×#72985

Splittings

Fitting

C₂×C₅×#95 ⋊ D₃

Subgroups

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

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

normal subgroups only

This group has 274 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)(6,16,27)(7,29,23,11,22,14)(8,25,9)(10,17,26)(12,28,21,20,24,13)(15,19,18);(6,7)(8,14)(9,13)(10,11)(12,15)(16,24)(17,28)(18,23)(19,21)(20,25)(22,26)(27,29)

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, 236407);