C₂²×C₇⋊D₇ #87663

order	392
isoclinism	isoclinic class of C₇⋊D₇
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³×C₇

Aliases

C₂²×C₇⋊D₇

Fitting, socle	C₂²×C₇² ⋊ C₂
derived, Sylow	C₇² ⋊ C₂³

	subgroup	G/H
center, hypercenter	C₂²	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂³
Frattini	C₁	G
Fitting, socle	C₂²×C₇²	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂²

160 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 196

A minimal faithful permutation representation — 3 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(392, 43);