D₈₇₃₅ #31775670

order	17470
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₈₇₃₅
unambiguous semidirect product	C₅⋊D₁₇₄₇
unambiguous semidirect product	C₁₇₄₇⋊D₅

Splittings

Fitting, socle, derived, Hall	C₅×C₁₇₄₇ ⋊ C₂
Sylow	C₁₇₄₇ ⋊ D₅
Sylow	C₅ ⋊ D₁₇₄₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₇₄₇	C₂
LCS	G ▷ C₅×C₁₇₄₇
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1752
transitive degree	μ_t(G) = 8735

A minimal faithful permutation representation — 2 generators on 1752 points:

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Polycyclic presentation:

2,5,1747|b^a=b^4,c^a=c^1746

Conjugacy classes & character table

4369 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₅×D₁₇₄₇, C₂×D₈₇₃₅
maximal normal subgroup of	D₅×D₁₇₄₇, C₂×D₈₇₃₅
maximal quotient of	Dic₈₇₃₅, C₂×D₈₇₃₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17470, 3);

D8735 #31775670