C₂²×D₃×C₈ #5736

order	192
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = C₂×D₃×#72209641 (order 18432) · Inn(G) = D₃ · Out(G) = C₂×#72209641
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂²×D₃×C₈

Fitting	C₂²×C₃×C₈ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂³×C₈

338 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 4 generators on 15 points:

(1,2)(3,4)(6,7);(5,6,7)(8,9,10,12,11,13,14,15);(3,4);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 1295);