C₇⋊D₃₂₉ #17987199

order	4606
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₇

Aliases

unambiguous semidirect product	C₇⋊D₃₂₉
unambiguous semidirect product	C₄₇⋊(C₇⋊D₇)

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₄₇	C₂
LCS	G ▷ C₇²×C₄₇
UCS	C₁

40 conjugacy classes of subgroups.

μ_t(G) = 2303

Polycyclic presentation:

2,7^2,47|b^a=b^6,c^a=c^6,d^a=d^46

1153 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4606, 10);