C₅×#4867 #11750366

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

Aliases

direct product

C₅×#4867

Splittings

Fitting	C₃×C₅×#106 ⋊ 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×#106	C₂
socle	C₂²×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₃	D₄
hypercenter	C₅×#106	D₃
hypocenter	C₃	C₅×#470
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#106

220 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 82 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)(15,22)(17,24)(18,25)(21,26)(23,28);(13,15,17,22,16,23,24,28)(14,18,20,26,19,21,27,25);(7,8)(10,12)(13,14)(15,21)(16,19)(17,20)(18,23)(22,25)(24,27)(26,28)

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×#69253, #14316375, C₅×#69314, …
maximal normal subgroup of	C₅×#69253, #14316375, C₅×#69314, …
maximal quotient of	C₅×#68541, C₅×#68551, C₅×#68543, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4561);