C₇×#1088⋊C₂ #13094583

order	1512
isoclinism	isoclinic class of #1088⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×#1088⋊C₂
unambiguous semidirect product	#1088⋊(C₂×C₇)
unambiguous semidirect product	(((C₃⋊D₃)⋊C₃)⋊C₂)⋊(C₂×C₇)

Fitting, Hall	C₇×H(3,𝔽₃) ⋊ D₄
Sylow	H(3,𝔽₃) ⋊ C₇×D₄

88 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 126

A minimal faithful permutation representation — 2 generators on 25 points:

(1,2,3,4,5,6,7)(8,10,20,18,12,19)(9,13,22)(11,17)(14,16,15,23,25,21);(8,9)(10,16)(11,14)(12,21)(13,17)(15,20)(18,25)(19,22)(23,24)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 480);