D₉₆₅₅ #34064524

order	19310
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₉₆₅₅
unambiguous semidirect product	C₅⋊D₁₉₃₁
unambiguous semidirect product	C₁₉₃₁⋊D₅

Splittings

Fitting, socle, derived, Hall	C₅×C₁₉₃₁ ⋊ C₂
Sylow	C₁₉₃₁ ⋊ D₅
Sylow	C₅ ⋊ D₁₉₃₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₉₃₁	C₂
LCS	G ▷ C₅×C₁₉₃₁
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1936
transitive degree	μ_t(G) = 9655

A minimal faithful permutation representation — 2 generators on 1936 points:

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Polycyclic presentation:

2,5,1931|b^a=b^4,c^a=c^1930

Conjugacy classes & character table

4829 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₅×D₁₉₃₁, C₂×D₉₆₅₅
maximal normal subgroup of	D₅×D₁₉₃₁, C₂×D₉₆₅₅
maximal quotient of	Dic₉₆₅₅, C₂×D₉₆₅₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19310, 5);

D9655 #34064524