C₂×C₃⋊D₃×C₈₂₃ #44444236

order	29628
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈₂₃ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₃⋊D₃×C₈₂₃
unambiguous semidirect product	(C₂×C₃)⋊(D₃×C₈₂₃)

	subgroup	G/H
center, hypercenter	C₂×C₈₂₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₈₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₈₂₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₈₂₃

60 conjugacy classes of subgroups.

μ_t(G) = 14814

9876 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29628, 45);