C₂×D₉₁₅₅ #49143643

order	36620
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₈₃₁₀
direct product	C₂×D₉₁₅₅
unambiguous semidirect product	(C₂×C₅)⋊D₁₈₃₁
unambiguous semidirect product	(C₂×C₁₈₃₁)⋊D₅

Splittings

Fitting, socle	C₂×C₅×C₁₈₃₁ ⋊ C₂
derived, Hall	C₅×C₁₈₃₁ ⋊ C₂²
Sylow	C₁₈₃₁ ⋊ C₂×D₅
Sylow	C₅ ⋊ C₂×D₁₈₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₉₁₅₅
commutator, cosocle, hypocenter	C₅×C₁₈₃₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₈₃₁	C₂
LCS	G ▷ C₅×C₁₈₃₁
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1838
transitive degree	μ_t(G) = 18310

A minimal faithful permutation representation — 2 generators on 1838 points:

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Conjugacy classes & character table

9158 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36620, 15);

C2×D9155 #49143643