D₂₁₇₇ #17983671

order	4354
automorphism	Aut(G) order 4049220
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₂₁₇₇
unambiguous semidirect product	C₇⋊D₃₁₁
unambiguous semidirect product	C₃₁₁⋊D₇

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₃₁₁	C₂
LCS	G ▷ C₇×C₃₁₁
UCS	C₁

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 318
transitive degree	μ_t(G) = 2177

Polycyclic presentation:

2,7,311|b^a=b^6,c^a=c^310

1090 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4354, 3);