C₁₃×#812 #11928083

order	1248
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₃×C₁₃ ⋊ M₃₂
Sylow	C₃ ⋊ C₁₃×M₃₂

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 624

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16)(18,22)(23,28)(24,29)(30,32);(15,16)(17,18,19,23,20,24,25,30,21,22,26,28,27,29,31,32)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 195);