C₂×D₇₇ #64574

order	308
isoclinism	isoclinic class of D₇₇
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₅₄
direct product	C₂×D₇₇
unambiguous semidirect product	(C₂×C₇)⋊D₁₁
unambiguous semidirect product	(C₂×C₁₁)⋊D₇

	subgroup	G/H
center, hypercenter	C₂	D₇₇
commutator, cosocle, hypocenter	C₇×C₁₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₁	C₂
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 154

A minimal faithful permutation representation — 2 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(308, 8);