D₉₃₃₅ #32916342

order	18670
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₉₃₃₅
unambiguous semidirect product	C₅⋊D₁₈₆₇
unambiguous semidirect product	C₁₈₆₇⋊D₅

Splittings

Fitting, socle, derived, Hall	C₅×C₁₈₆₇ ⋊ C₂
Sylow	C₁₈₆₇ ⋊ D₅
Sylow	C₅ ⋊ D₁₈₆₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₈₆₇	C₂
LCS	G ▷ C₅×C₁₈₆₇
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1872
transitive degree	μ_t(G) = 9335

A minimal faithful permutation representation — 2 generators on 1872 points:

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Polycyclic presentation:

2,5,1867|b^a=b^4,c^a=c^1866

Conjugacy classes & character table

4669 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₅×D₁₈₆₇, C₂×D₉₃₃₅
maximal normal subgroup of	D₅×D₁₈₆₇, C₂×D₉₃₃₅
maximal quotient of	Dic₉₃₃₅, C₂×D₉₃₃₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18670, 3);

D9335 #32916342