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C₂×D₅×#4020 #72269353

order	3200
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

C₂×D₅×#4020

Splittings

Fitting	C₂×C₄²×C₅² ⋊ C₂²
Sylow	C₅² ⋊ C₂²×#127

Subgroups

	subgroup	G/H
center	C₂³	C₂²×D₅²
commutator, cosocle	C₂²×C₅²	C₂⁵
Frattini	C₂²	C₂³×D₅²
Fitting	C₂×C₄²×C₅²	C₂²
socle	C₂³×C₅²	C₂⁴
hypercenter	C₂×C₄²	D₅²
hypocenter	C₅²	C₂²×#127
LCS	G ▷ C₂²×C₅² ▷ C₅²
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

6498 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 320

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.