C₅×#5812 #11756197

order	960
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₅ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₅×#5812

Splittings

Hall	C₃×C₅ ⋊ #519
Sylow	C₃ ⋊ C₅×#519

Subgroups

	subgroup	G/H
center	C₂²×C₅	C₂³×D₃
commutator	C₂×C₃	C₂³×C₄×C₅
Frattini	C₂²	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×Q₈	C₂
socle	C₂²×C₃×C₅	C₂⁴
prime radical	C₂³×C₃×C₅	C₂³
cosocle	C₂²×C₃	C₂⁴×C₅
hypercenter	C₂²×C₅×Q₈	D₃
hypocenter	C₃	C₅×#519
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₅×Q₈

532 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 4 generators on 28 points:

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

Conjugacy classes & character table

270 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×#70101, #14298699, C₅×#69672, …
maximal normal subgroup of	C₅×#70101, #14298699, C₅×#69672, …
maximal quotient of	C₅×#82144, C₅×#82450, C₅×#84062, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10392);

C5×#5812 #11756197