C₇×#392⋊C₃ #13055048

order	1344
isoclinism	isoclinic class of #392⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×#392⋊C₃
unambiguous semidirect product	#392⋊(C₃×C₇)

Fitting, Hall	C₇×#392 ⋊ C₃
Sylow	#392 ⋊ C₃×C₇

	subgroup	G/H
center, hypercenter	C₂×C₇	#127⋊C₃
commutator, cosocle, hypocenter	#95	C₂×C₃×C₇
Frattini	C₂³	C₂×C₇×A₄
Fitting	C₇×#392	C₃
socle	C₂³×C₇	C₂×A₄
LCS	G ▷ #95
UCS	C₁ ◁ C₂×C₇

134 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)(8,13,18,11,10,17,12,15,14,9,16,19);(8,11,12,9)(13,15)(14,17)(18,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4337);