C₃²×D₆₈ #11927520

order	1224
isoclinism	isoclinic class of Dic₃₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃²×D₆₈
unambiguous semidirect product	C₄⋊(C₃²×D₁₇)

96 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 612

A minimal faithful permutation representation — 2 generators on 27 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1224, 93);