C₂×C₃×D₇×C₂₂₃ #34035477

order	18732
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₂₂₃ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₃×D₇×C₂₂₃

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₂₃	D₇
commutator, cosocle, hypocenter	C₇	C₂²×C₃×C₂₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₂₂₃	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₂₂₃

40 conjugacy classes of subgroups.

μ_t(G) = 9366

6690 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18732, 63);