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D₇×#4741 #72244276

order	2688
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁷

Aliases

Splittings

Fitting	C₃×C₇×#99 ⋊ C₂²
Hall	C₃×C₇ ⋊ C₂×B(4,𝔽₂)
Sylow	C₇ ⋊ C₂×#4741
Sylow	C₃ ⋊ D₇×B(4,𝔽₂)

Subgroups

	subgroup	G/H
center	C₂	D₇×#882
commutator, cosocle	C₂³×C₃×C₇	C₂⁴
Frattini	C₂³	C₂²×D₃×D₇
Fitting	C₃×C₇×#99	C₂²
socle	C₂×C₃×C₇	C₂×#120
hypercenter	#99	D₃×D₇
hypocenter	C₃×C₇	C₂×B(4,𝔽₂)
LCS	G ▷ C₂³×C₃×C₇ ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ #99

2036 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 168

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×D₇×B(4,𝔽₂), AGL(1,𝔽₇)×#4741
maximal normal subgroup of	D₃×D₇×B(4,𝔽₂), AGL(1,𝔽₇)×#4741

GAP

Past the SmallGroups library coverage — no SmallGroups id.