C₂×C₂₃×3₋¹⁺² #11927869

order	1242
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₂₃×3₋¹⁺²
unambiguous semidirect product	(C₂×C₉)⋊(C₃×C₂₃)
unambiguous semidirect product	(C₂×C₉×C₂₃)⋊C₃

	subgroup	G/H
center, socle	C₂×C₃×C₂₃	C₃²
commutator, Frattini, cosocle	C₃	C₂×C₃²×C₂₃
prime radical	C₂×C₃²×C₂₃	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₂₃ ◁ G

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 414

A minimal faithful permutation representation — 2 generators on 34 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1242, 22);