D₂₂₇₇ #17986910

order	4554
automorphism	Aut(G) order 3005640
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₂₂₇₇
unambiguous semidirect product	C₉⋊D₂₅₃
unambiguous semidirect product	C₁₁⋊D₂₀₇
unambiguous semidirect product	C₂₃⋊D₉₉

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₁×C₂₃	C₂
Frattini	C₃	D₇₅₉
socle	C₃×C₁₁×C₂₃	D₃
LCS	G ▷ C₉×C₁₁×C₂₃
UCS	C₁

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 2277

Polycyclic presentation:

2,3,11,23,3|b^3=e^2,b^a=b^2e,c^a=c^10,d^a=d^22,e^a=e^2

1140 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4554, 12);