C₃×D₇₇ #90761

order	462
isoclinism	isoclinic class of D₇₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₇₇
unambiguous semidirect product	C₁₁⋊(C₃×D₇)

	subgroup	G/H
center, hypercenter	C₃	D₇₇
commutator, cosocle, hypocenter	C₇×C₁₁	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁	C₂
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₃

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 231

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(462, 7);