C₂×C₃×C₇×H(3,𝔽₃) #11765804

order	1134
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃³×C₇ · Schur multiplier (H₂) = C₃⁴

Aliases

direct product	C₂×C₃×C₇×H(3,𝔽₃)
unambiguous semidirect product	(C₂×C₃²)⋊(C₃²×C₇)

	subgroup	G/H
center, socle	C₂×C₃²×C₇	C₃²
commutator, Frattini, cosocle	C₃	C₂×C₃³×C₇
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂×C₃²×C₇ ◁ G

224 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 378

A minimal faithful permutation representation — 3 generators on 21 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1134, 234);