C₅×#5479 #11755864

order	960
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₅×#5479

Splittings

Fitting	C₂×C₃×C₄²×C₅ ⋊ C₂
Hall	C₃×C₅ ⋊ #529
Sylow	C₃ ⋊ C₅×#529

Subgroups

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₅
Frattini	C₂²	C₂³×C₅×D₃
Fitting	C₂×C₃×C₄²×C₅	C₂
socle	C₂²×C₃×C₅	C₂⁴
prime radical	C₅×#930	C₂
hypercenter	C₂×C₄²×C₅	D₃
hypocenter	C₃	C₅×#529
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅

468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×#70759, C₅×#70760, #14281886, …
maximal normal subgroup of	C₅×#70759, C₅×#70760, #14281886, …
maximal quotient of	C₅×#82060, C₅×#82065, C₅×#73299, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10059);

C5×#5479 #11755864