C₇²×D₁₃⋊C₃ #16838433

order	3822
isoclinism	isoclinic class of D₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₇² · Schur multiplier (H₂) = C₇

Aliases

direct product	C₇²×D₁₃⋊C₃
unambiguous semidirect product	D₁₃⋊(C₃×C₇²)
unambiguous semidirect product	(C₁₃⋊C₃)⋊(C₂×C₇²)

	subgroup	G/H
center, hypercenter	C₇²	D₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃×C₇²
Frattini	C₁	G
Fitting, socle	C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₇²

80 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 27 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3822, 26);