C₅×#4853 #11750352

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

Aliases

direct product

C₅×#4853

Splittings

Hall	C₃×C₅ ⋊ #441
Sylow	C₃ ⋊ C₅×#441

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, prime radical	C₂²×C₃×C₅	C₂×D₄
cosocle	C₂×C₃×C₄	C₂³×C₅
hypercenter	C₅×#106	D₃
hypocenter	C₃	C₅×#441
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#106

216 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 960

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

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×#69248, C₅×#69309, #14315769, …
maximal normal subgroup of	C₅×#69248, C₅×#69309, #14315769, …
maximal quotient of	C₅×#68517, C₅×#68522, C₅×#68524, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4547);