Finite Group Databasebeta

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D₇×C₃⋊D₃×#127 #72246404

order	8064
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹×C₃×C₄

Aliases

D₇×C₃⋊D₃×#127

Splittings

Fitting	C₃²×C₇×#127 ⋊ C₂²
Hall	C₃²×C₇ ⋊ C₂²×#127
Sylow	C₃² ⋊ C₂×D₇×#127
Sylow	C₇ ⋊ C₂×C₃⋊D₃×#127

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₇×C₃⋊D₃
commutator, socle, cosocle	C₂²×C₃²×C₇	C₂⁵
Fitting	C₃²×C₇×#127	C₂²
hypercenter	#127	D₇×C₃⋊D₃
hypocenter	C₃²×C₇	C₂²×#127
LCS	G ▷ C₂²×C₃²×C₇ ▷ C₃²×C₇
UCS	C₁ ◁ C₂² ◁ #127

18000 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1008

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃⋊D₃×#127×AGL(1,𝔽₇), D₇×#11864777
maximal normal subgroup of	C₃⋊D₃×#127×AGL(1,𝔽₇), D₇×#11864777

GAP

Past the SmallGroups library coverage — no SmallGroups id.