C₃³×D₂₃ #11927870

order	1242
isoclinism	isoclinic class of D₂₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃³ · Schur multiplier (H₂) = C₃³

Aliases

direct product	C₃³×D₂₃
unambiguous semidirect product	C₂₃⋊(C₂×C₃³)

Splittings

Fitting, socle, Hall	C₃³×C₂₃ ⋊ C₂
derived, Sylow	C₂₃ ⋊ C₂×C₃³

Subgroups

	subgroup	G/H
center, hypercenter	C₃³	D₂₃
commutator, cosocle, hypocenter	C₂₃	C₂×C₃³
Frattini	C₁	G
Fitting, socle	C₃³×C₂₃	C₂
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₃³

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 621

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1242, 23);

C33×D23 #11927870