C₂×D₉₀₀₅ #49112883

order	36020
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₈₀₁₀
direct product	C₂×D₉₀₀₅
unambiguous semidirect product	(C₂×C₅)⋊D₁₈₀₁
unambiguous semidirect product	(C₂×C₁₈₀₁)⋊D₅

Splittings

Fitting, socle	C₂×C₅×C₁₈₀₁ ⋊ C₂
derived, Hall	C₅×C₁₈₀₁ ⋊ C₂²
Sylow	C₁₈₀₁ ⋊ C₂×D₅
Sylow	C₅ ⋊ C₂×D₁₈₀₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₉₀₀₅
commutator, cosocle, hypocenter	C₅×C₁₈₀₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₈₀₁	C₂
LCS	G ▷ C₅×C₁₈₀₁
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1808
transitive degree	μ_t(G) = 18010

A minimal faithful permutation representation — 2 generators on 1808 points:

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Conjugacy classes & character table

9008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36020, 20);

C2×D9005 #49112883