C₁₃×C₇⋊D₇ #11929704

order	1274
isoclinism	isoclinic class of C₇⋊D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₁₃×C₇⋊D₇
unambiguous semidirect product	C₇⋊(C₁₃×D₇)

Fitting, socle, Hall	C₇²×C₁₃ ⋊ C₂
derived, Sylow	C₇² ⋊ C₂×C₁₃

	subgroup	G/H
center, hypercenter	C₁₃	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₇²×C₁₃	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₁₃

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 637

A minimal faithful permutation representation — 3 generators on 27 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1274, 8);