C₇×C₄⋊Dic₉ #11758912

order	1008
isoclinism	isoclinic class of Dic₁₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×C₄⋊Dic₉
unambiguous semidirect product	C₄⋊(C₇×Dic₉)

Hall	C₇×C₉ ⋊ C₄⋊C₄
Sylow	C₉ ⋊ C₇×C₄⋊C₄

78 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 1008

A minimal faithful permutation representation — 2 generators on 24 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1008, 83);