C₄⋊(C₇⋊D₇) #87650

order	392
isoclinism	isoclinic class of #87648
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₇

Aliases

C₄⋊(C₇⋊D₇)

Fitting	C₄×C₇² ⋊ C₂
Sylow	C₇² ⋊ D₄

80 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)(12,13,15,17,18,16,14);(2,4)(6,7)(8,9)(10,11)(13,14)(15,16)(17,18);(5,6,8,10,11,9,7)

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(392, 30);