C₁₃×C₄⋊(C₃⋊C₈) #11928075

order	1248
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×C₄⋊(C₃⋊C₈)
unambiguous semidirect product	C₄⋊(C₁₃×C₃⋊C₈)

Hall	C₃×C₁₃ ⋊ C₄⋊C₈
Sylow	C₃ ⋊ C₁₃×C₄⋊C₈

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 1248

A minimal faithful permutation representation — 2 generators on 28 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16)(17,18,19,20);(15,16)(18,20)(21,22,23,25,24,26,27,28)

468 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 187);