C₂×C₇²×C₁₃⋊C₃ #16838488

order	3822
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₇² · Schur multiplier (H₂) = C₇

Aliases

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

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

80 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 1274

A minimal faithful permutation representation — 2 generators on 29 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3822, 81);