D₇×Dic₇ #87638

order	392
isoclinism	isoclinic class of D₇²
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₇×Dic₇
unambiguous semidirect product	(C₇×D₇)⋊C₄

C₇² ⋊ C₂×C₄

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇²
commutator, hypocenter	C₇²	C₂×C₄
Fitting, socle, cosocle	C₂×C₇²	C₂²
prime radical	C₂×C₇×D₇	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂

41 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 56

A minimal faithful permutation representation — 2 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(392, 18);