C₇×#983 #10621490

order	672
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₇×Q₈ ⋊ D₃

	subgroup	G/H
center, socle	C₂×C₇	C₂×S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂²×C₇
Frattini	C₂	C₂×C₇×S₄
Fitting	C₂×C₇×Q₈	D₃
hypercenter	C₂²×C₇	S₄
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₇ ◁ C₂²×C₇

78 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 112

A minimal faithful permutation representation — 2 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 1072);