C₇⋊Dic₁₆₁ #17985200

order	4508
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₇

Aliases

unambiguous semidirect product	C₇⋊Dic₁₆₁
unambiguous semidirect product	C₂₃⋊(C₇⋊Dic₇)

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₇⋊D₁₆₁
commutator, hypocenter	C₇²×C₂₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₇²×C₂₃	C₂
LCS	G ▷ C₇²×C₂₃
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

μ_t(G) = 4508

Polycyclic presentation:

2,7^2,23,2|a^2=e,b^a=b^6,c^a=c^6,d^a=d^22

1130 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4508, 15);