C₃×#10621463 #72277610

order	2016
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

non-solvable

Aliases

direct product

C₃×#10621463

Subgroups

	subgroup	G/H
center, Fitting, socle, hypercenter	C₂×C₃	SO(3,𝔽₇)
commutator, cosocle, hypocenter	SL(2,𝔽₇)	C₂×C₃
Frattini	C₂	C₃×SO(3,𝔽₇)
prime radical	C₃×SL(2,𝔽₇)	C₂
LCS	G ▷ SL(2,𝔽₇)
UCS	C₁ ◁ C₂×C₃

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 2 generators on 35 points:

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

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#13062004
maximal normal subgroup of	C₃×#13062004
maximal quotient of	C₃×#13057024

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((4,6,14,28,21,33,5,10,16,30,22,24,18,27,32,35)(7,17,26,15,31,29,8,19,25,12,20,34,9,23,11,13), (1,2,3)(4,7,18)(5,11,26)(6,15,19)(8,20,32)(10,24,29)(13,30,34)(16,25,21)(23,35,28));

C3×#10621463 #72277610