C₂×D₆₈ #63251

order	272
isoclinism	isoclinic class of Dic₃₄
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

C₂×D₆₈

Fitting	C₂×C₄×C₁₇ ⋊ C₂
Sylow	C₁₇ ⋊ C₂×D₄

54 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 136

A minimal faithful permutation representation — 3 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(272, 38);