D₇×C₁₇₂₃ #37563207

order	24122
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₇×C₁₇₂₃
unambiguous semidirect product	C₇⋊(C₂×C₁₇₂₃)

Fitting, socle, Hall	C₇×C₁₇₂₃ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₁₇₂₃

	subgroup	G/H
center, hypercenter	C₁₇₂₃	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₁₇₂₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₇₂₃	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₁₇₂₃

8 conjugacy classes of subgroups.

μ_t(G) = 12061

8615 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24122, 3);