C₃×#65813 #11755490

order	960
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃×#65813

Splittings

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

Subgroups

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂
socle	C₂²×C₃×C₅	C₂⁴
prime radical	C₃×#4076	C₂
hypercenter	C₂×C₃×C₄²	D₅
hypocenter	C₅	C₃×#529
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄²

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×#10601552, C₃×#10601553, #14281884, …
maximal normal subgroup of	C₃×#10601552, C₃×#10601553, #14281884, …
maximal quotient of	C₃×#10613791, C₃×#10613796, C₃×#10605030, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9685);

C3×#65813 #11755490