C₅×#4824 #11750323

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

Aliases

direct product

C₅×#4824

Splittings

Fitting	C₃×C₅×#104 ⋊ C₂
Hall	C₃×C₅ ⋊ #443
Sylow	C₃ ⋊ C₅×#443

Subgroups

	subgroup	G/H
center	C₄×C₅	D₃×D₄
commutator	C₃×C₄	C₂²×C₄×C₅
Frattini	C₂×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#104	C₂
socle	C₂×C₃×C₅	C₄×D₄
prime radical	C₅×#950	C₂
cosocle	C₂×C₃×C₄	C₂³×C₅
hypercenter	C₅×#104	D₃
hypocenter	C₃	C₅×#443
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#104

212 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 90 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)(9,12,13,20,15,21,14,11)(10,16,17,23,18,24,22,19);(9,11)(10,16)(12,13)(14,21)(15,20)(17,23)(18,24)(19,22);(7,8)(9,10)(11,19)(12,16)(13,17)(14,22)(15,18)(20,23)(21,24)

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#443, C₂×C₅×#4824, D₅×#4824, …
maximal normal subgroup of	C₅×D₃×#443, C₂×C₅×#4824, D₅×#4824, …
maximal quotient of	C₅×#68148, C₅×#68212, C₅×#68149, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4518);