C₂×D₁₁₉ #90918

order	476
isoclinism	isoclinic class of D₁₁₉
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₂₃₈
direct product	C₂×D₁₁₉
unambiguous semidirect product	(C₂×C₇)⋊D₁₇
unambiguous semidirect product	(C₂×C₁₇)⋊D₇

	subgroup	G/H
center, hypercenter	C₂	D₁₁₉
commutator, cosocle, hypocenter	C₇×C₁₇	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₇	C₂
LCS	G ▷ C₇×C₁₇
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 238

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2)(3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26);(4,9)(5,8)(6,7)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(476, 10);