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D₃×D₇×#127 #72244229

order	2688
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

D₃×D₇×#127

Splittings

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

Subgroups

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

6000 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 336

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#127×AGL(1,𝔽₇), D₃×D₇×#453, D₇×C₃⋊D₃×#127
maximal normal subgroup of	D₃×#127×AGL(1,𝔽₇), D₃×D₇×#453
maximal quotient of	D₇×C₃⋊D₃×#127

GAP

Past the SmallGroups library coverage — no SmallGroups id.