C₁₃×ΓL(1,𝔽₈)×A₅ #30655803

order	16380
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×ΓL(1,𝔽₈)×A₅
unambiguous semidirect product	C₇⋊(C₃×C₁₃×A₅)
unambiguous semidirect product	(C₇×A₅)⋊(C₃×C₁₃)

84 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 455

A minimal faithful permutation representation — 2 generators on 25 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 853);