C₇×D₆₈ #11745758

order	952
isoclinism	isoclinic class of Dic₃₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×D₆₈
unambiguous semidirect product	C₄⋊(C₇×D₁₇)

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 476

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(952, 16);