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C₃×D₇×#453 #72244283

order	2688
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶

Aliases

C₃×D₇×#453

Splittings

Fitting	C₃×C₇×#453 ⋊ C₂
Hall	C₃×C₇ ⋊ C₂×#453
Sylow	C₇ ⋊ C₂×C₃×#453

Subgroups

	subgroup	G/H
center	C₂×C₃	D₇×#120
commutator, cosocle	C₂×C₄×C₇	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₇
Fitting	C₃×C₇×#453	C₂
socle	C₂×C₃×C₇	C₂×#120
hypercenter	C₃×#453	D₇
hypocenter	C₇	C₂×C₃×#453
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#453

1688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 168

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×D₇×#453, #72245962, C₃×AGL(1,𝔽₇)×#453, …
maximal normal subgroup of	D₃×D₇×#453, C₃×AGL(1,𝔽₇)×#453
maximal quotient of	#72245962, #453×ΓL(1,𝔽₈)⋊D₇, C₃×D₇×#5077

GAP

Past the SmallGroups library coverage — no SmallGroups id.