C₇×#95⋊C₃ #10620552

order	672
isoclinism	isoclinic class of #95⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×#95⋊C₃
unambiguous semidirect product	#95⋊(C₃×C₇)

Fitting, Hall	C₇×#95 ⋊ C₃
derived, Sylow	#95 ⋊ C₃×C₇

	subgroup	G/H
center, hypercenter	C₂×C₇	C₄²⋊C₃
commutator, cosocle, hypocenter	#95	C₃×C₇
Frattini	C₂³	C₇×A₄
Fitting	C₇×#95	C₃
socle	C₂³×C₇	A₄
LCS	G ▷ #95
UCS	C₁ ◁ C₂×C₇

42 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 84

A minimal faithful permutation representation — 2 generators on 19 points:

(1,2,3,4,5,6,7)(8,9,12)(10,14,19)(11,15,18)(13,17,16);(8,10,11,16)(12,17)(13,14)(18,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 134);