C₂₃×C₃⋊D₉ #11927863

order	1242
isoclinism	isoclinic class of C₃⋊D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₂₃×C₃⋊D₉
unambiguous semidirect product	C₃⋊(D₉×C₂₃)
unambiguous semidirect product	C₉⋊(D₃×C₂₃)

Fitting, Hall	C₃×C₉×C₂₃ ⋊ C₂
derived, Sylow	C₃×C₉ ⋊ C₂×C₂₃

	subgroup	G/H
center, hypercenter	C₂₃	C₃⋊D₉
commutator, cosocle, hypocenter	C₃×C₉	C₂×C₂₃
Frattini	C₃	C₃⋊D₃×C₂₃
Fitting	C₃×C₉×C₂₃	C₂
socle	C₃²×C₂₃	D₃
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₂₃

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 621

A minimal faithful permutation representation — 3 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,26)(28,30)(29,33)(31,32)(34,35);(24,25,26);(27,35,30,33,32,31,29,28,34)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1242, 16);