C₁₃×C₂²⋊Dic₇ #13089809

order	1456
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₁₃×C₂²⋊Dic₇
unambiguous semidirect product	C₂²⋊(C₁₃×Dic₇)

Hall	C₇×C₁₃ ⋊ C₂²⋊C₄
Sylow	C₇ ⋊ C₁₃×C₂²⋊C₄

68 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 728

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1456, 63);