C₅×#4816 #11750315

order	960
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#4816

Splittings

Fitting	C₃×C₅×#103 ⋊ C₂
Hall	C₃×C₅ ⋊ #470
Sylow	C₃ ⋊ C₅×#470

Subgroups

	subgroup	G/H
center	C₂²×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂³×C₅
Frattini	C₂×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#103	C₂
socle	C₂²×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₃	D₄
hypercenter	C₅×#103	D₃
hypocenter	C₃	C₅×#470
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#103

220 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 78 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)(13,15,17,22)(14,19,18,25)(16,24,23,21)(20,27,26,28);(9,10,11,12)(14,18)(15,21)(16,23)(19,27)(22,24)(25,28);(7,8)(10,12)(13,14)(15,19)(16,20)(17,18)(21,28)(22,25)(23,26)(24,27)

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#470, C₂×C₅×#4816, D₅×#4816, …
maximal normal subgroup of	C₅×D₃×#470, C₂×C₅×#4816, D₅×#4816, …
maximal quotient of	C₅×#68449, C₅×#68473, C₅×#68501, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4510);