C₂×C₁₃×C₃⋊D₃×C₂₃ #24924586

order	10764
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃×C₂₃ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₁₃×C₃⋊D₃×C₂₃
unambiguous semidirect product	(C₂×C₃)⋊(D₃×C₁₃×C₂₃)

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₂₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₁₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃×C₂₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₁₃×C₂₃

120 conjugacy classes of subgroups.

3588 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 122);