C₃×#64667 #11746024

order	960
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₆ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×#64667

Splittings

Fitting	C₃×C₅×C₃₂ ⋊ C₂
Hall	C₃×C₅ ⋊ M₆₄
Sylow	C₅ ⋊ C₃×M₆₄

Subgroups

	subgroup	G/H
center	C₃×C₁₆	C₂×D₅
commutator	C₂×C₅	C₂×C₃×C₁₆
Frattini	C₁₆	C₂×C₃×D₅
Fitting	C₃×C₅×C₃₂	C₂
socle	C₂×C₃×C₅	C₂×C₁₆
prime radical	C₂×C₃×D₅	C₁₆
cosocle	C₅×C₁₆	C₂²×C₃
hypercenter	C₃×C₃₂	D₅
hypocenter	C₅	C₃×M₆₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₁₆ ◁ C₃×C₃₂

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3)(4,5,7,8,6)(9,10,11,16,12,17,19,28,13,18,20,29,22,30,31,38,14,15,21,25,23,26,32,35,24,27,33,36,34,37,39,40);(5,6)(7,8)(10,15)(16,25)(17,26)(18,27)(28,35)(29,36)(30,37)(38,40)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×#10598487, #14279225, C₃×#10598488, …
maximal normal subgroup of	C₃×#10598487, #14279225, C₃×#10598488, …
maximal quotient of	C₃×#10598080, C₃×#10598085, C₃×#10598081, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 219);

C3×#64667 #11746024