C₇×C₄⋊Dic₁₃ #13089787

order	1456
isoclinism	isoclinic class of Dic₂₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×C₄⋊Dic₁₃
unambiguous semidirect product	C₄⋊(C₇×Dic₁₃)

Hall	C₇×C₁₃ ⋊ C₄⋊C₄
Sylow	C₁₃ ⋊ C₇×C₄⋊C₄

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 1456

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1456, 41);