D₁₅₇₇₇ #44538806

order	31554
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₅₇₇₇
unambiguous semidirect product	C₉⋊D₁₇₅₃
unambiguous semidirect product	C₁₇₅₃⋊D₉

Splittings

Fitting, derived, Hall	C₉×C₁₇₅₃ ⋊ C₂
Sylow	C₁₇₅₃ ⋊ D₉
Sylow	C₉ ⋊ D₁₇₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₇₅₃	C₂
Frattini	C₃	D₅₂₅₉
socle	C₃×C₁₇₅₃	D₃
LCS	G ▷ C₉×C₁₇₅₃
UCS	C₁

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1762
transitive degree	μ_t(G) = 15777

A minimal faithful permutation representation — 2 generators on 1762 points:

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Polycyclic presentation:

2,3,1753,3|b^3=d^2,b^a=b^2d,c^a=c^1752,d^a=d^2

Conjugacy classes & character table

7890 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₅₇₇₇
maximal normal subgroup of	C₂×D₁₅₇₇₇
maximal quotient of	Dic₁₅₇₇₇, C₂×D₁₅₇₇₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31554, 6);

D15777 #44538806