Finite Group Databasebeta

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D₅×C₃⋊D₃×#127 #72231617

order	5760
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹×C₃×C₄

Aliases

D₅×C₃⋊D₃×#127

Splittings

Fitting	C₃²×C₅×#127 ⋊ C₂²
Hall	C₃²×C₅ ⋊ C₂²×#127
Sylow	C₃² ⋊ C₂×D₅×#127
Sylow	C₅ ⋊ C₂×C₃⋊D₃×#127

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₅×C₃⋊D₃
commutator, socle, cosocle	C₂²×C₃²×C₅	C₂⁵
Fitting	C₃²×C₅×#127	C₂²
hypercenter	#127	D₅×C₃⋊D₃
hypocenter	C₃²×C₅	C₂²×#127
LCS	G ▷ C₂²×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₂² ◁ #127

18000 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 720

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃⋊D₃×AGL(1,𝔽₅)×#127
maximal normal subgroup of	C₃⋊D₃×AGL(1,𝔽₅)×#127

GAP

Past the SmallGroups library coverage — no SmallGroups id.