Finite Group Databasebeta

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D₇×#11669 #72259865

order	3584
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

Splittings

Fitting	C₇×#11669 ⋊ C₂
Sylow	C₇ ⋊ C₂×#11669

Subgroups

	subgroup	G/H
center	C₄	D₇×#418
commutator	C₂×C₇×C₈	C₂³×C₄
Frattini	C₄×C₈	C₂³×D₇
Fitting	C₇×#11669	C₂
socle	C₂×C₇	C₂×#1490
prime radical	D₇×#575	C₄
cosocle	C₄×C₇×C₈	C₂⁴
hypercenter	#11669	D₇
hypocenter	C₇	C₂×#11669
LCS	G ▷ C₂×C₇×C₈ ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×M₁₆ ◁ #11669

1938 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 112

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₇×#489347
maximal normal subgroup of	D₇×#489347

GAP

Past the SmallGroups library coverage — no SmallGroups id.