Finite Group Databasebeta

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D₇×#8534 #72259990

order	3584
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

Splittings

Fitting	C₇×#8534 ⋊ C₂
Sylow	C₇ ⋊ C₂×#8534

Subgroups

	subgroup	G/H
center	C₂²	D₇×#379
commutator	C₂⁴×C₇	C₂³×C₄
Frattini	C₂⁵	C₂³×D₇
Fitting	C₇×#8534	C₂
socle	C₂²×C₇	C₂×#379
prime radical	D₇×#3484	C₂
cosocle	C₂⁵×C₇	C₂⁴
hypercenter	#8534	D₇
hypocenter	C₇	C₂×#8534
LCS	G ▷ C₂⁴×C₇ ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ #8534

9744 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 112

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.