#5997⋊C₂ #87657

order	392
isoclinism	isoclinic class of #5997⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	#5997⋊C₂
unambiguous semidirect product	D₇²⋊C₂

C₇² ⋊ D₄

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle	C₇⋊D₇	C₂²
Fitting, socle, hypocenter	C₇²	D₄
LCS	G ▷ C₇⋊D₇ ▷ C₇²
UCS	C₁

28 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 14

A minimal faithful permutation representation — 2 generators on 14 points:

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

Polycyclic presentation:

2^3,7^2|b^a=bc,d^a=d^6,d^b=e,e^b=d,d^c=d^6,e^c=e^6

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(392, 37);