C₂³×D₁₂ #5953

order	192
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) order 4128768
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂³×D₁₂

Fitting	C₂³×C₃×C₄ ⋊ C₂
Sylow	C₃ ⋊ C₂³×D₄

1362 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 5 generators on 13 points:

(7,8,9)(10,11,12,13);(1,2)(3,4)(5,6)(8,9)(11,13);(5,6);(3,4);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 1512);