C₇×#4318 #11927653

order	1232
isoclinism	isoclinic class of Dic₂₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₇ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₇×C₁₁ ⋊ M₁₆
Sylow	C₁₁ ⋊ C₇×M₁₆

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 616

A minimal faithful permutation representation — 2 generators on 26 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1232, 36);