D₉₃₈₅ #34037325

order	18770
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₉₃₈₅
unambiguous semidirect product	C₅⋊D₁₈₇₇
unambiguous semidirect product	C₁₈₇₇⋊D₅

Splittings

Fitting, socle, derived, Hall	C₅×C₁₈₇₇ ⋊ C₂
Sylow	C₁₈₇₇ ⋊ D₅
Sylow	C₅ ⋊ D₁₈₇₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₈₇₇	C₂
LCS	G ▷ C₅×C₁₈₇₇
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1882
transitive degree	μ_t(G) = 9385

A minimal faithful permutation representation — 2 generators on 1882 points:

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Polycyclic presentation:

2,5,1877|b^a=b^4,c^a=c^1876

Conjugacy classes & character table

4694 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	#49176263, #49176264, D₅×D₁₈₇₇, …
maximal normal subgroup of	#49176263, #49176264, D₅×D₁₈₇₇, …
maximal quotient of	Dic₉₃₈₅, C₂×D₉₃₈₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18770, 3);

D9385 #34037325