C₅×#4860 #11750359

order	960
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₅×#4860

Splittings

Fitting	C₃×C₅×#106 ⋊ C₂
Hall	C₃×C₅ ⋊ #427
Sylow	C₃ ⋊ C₅×#427

Subgroups

	subgroup	G/H
center	C₂²×C₅	D₃×D₄
commutator	C₃×C₄	C₂²×C₄×C₅
Frattini	C₂×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#106	C₂
socle	C₂²×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₃	D₄
cosocle	C₂×C₃×C₄	C₂³×C₅
hypercenter	C₅×#106	D₃
hypocenter	C₃	C₅×#427
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#106

228 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 28
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×#69251, #14314143, C₅×#69312, …
maximal normal subgroup of	C₅×#69251, #14314143, C₅×#69312, …
maximal quotient of	C₅×#68527, C₅×#68530, C₅×#68533, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4554);