C₃×C₄⋊#1055 #11928034

order	1248
isoclinism	isoclinic class of Dic₂₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₈ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×C₄⋊#1055
unambiguous semidirect product	C₄⋊(C₃×#1055)

Hall	C₃×C₁₃ ⋊ C₄⋊C₈
Sylow	C₁₃ ⋊ C₃×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)(4,5,7,9,11,13,15,16,14,12,10,8,6)(17,18,19,20);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(18,20)(21,22,23,25,24,26,27,28)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 146);