C₅×#5144 #11750643

order	960
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#5144

Splittings

Fitting	C₃×C₅×#131 ⋊ C₂
Hall	C₃×C₅ ⋊ #443
Sylow	C₃ ⋊ C₅×#443

Subgroups

	subgroup	G/H
center	C₅×C₈	#67
commutator	C₃×C₄	C₂²×C₄×C₅
Frattini	C₂×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#131	C₂
socle	C₂×C₃×C₅	C₄×D₄
prime radical	C₅×#950	C₂
cosocle	C₂×C₃×C₄	C₂³×C₅
hypercenter	C₅×#131	D₃
hypocenter	C₃	C₅×#443
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₅×C₈ ◁ C₂×C₅×C₈ ◁ C₅×#131

212 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 24
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×#69122, C₅×#71452, #14315211, …
maximal normal subgroup of	C₅×#69122, C₅×#71452, #14315211, …
maximal quotient of	C₅×C₈×#213, C₅×C₈×#214, C₅×C₈×#215, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4838);