D₈₇₉₅ #31798482

order	17590
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₈₇₉₅
unambiguous semidirect product	C₅⋊D₁₇₅₉
unambiguous semidirect product	C₁₇₅₉⋊D₅

Splittings

Fitting, socle, derived, Hall	C₅×C₁₇₅₉ ⋊ C₂
Sylow	C₁₇₅₉ ⋊ D₅
Sylow	C₅ ⋊ D₁₇₅₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₇₅₉	C₂
LCS	G ▷ C₅×C₁₇₅₉
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1764
transitive degree	μ_t(G) = 8795

A minimal faithful permutation representation — 2 generators on 1764 points:

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Polycyclic presentation:

2,5,1759|b^a=b^4,c^a=c^1758

Conjugacy classes & character table

4399 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₅×D₁₇₅₉, C₂×D₈₇₉₅
maximal normal subgroup of	D₅×D₁₇₅₉, C₂×D₈₇₉₅
maximal quotient of	Dic₈₇₉₅, C₂×D₈₇₉₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17590, 3);

D8795 #31798482