Finite Group Databasebeta

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D₇×#12310 #72259783

order	3584
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

Splittings

Fitting	C₇×#12310 ⋊ C₂
Sylow	C₇ ⋊ C₂×#12310

Subgroups

	subgroup	G/H
center	C₂	D₇×#1619
commutator, cosocle	C₄×C₇×C₈	C₂⁴
Frattini	C₄×C₈	C₂³×D₇
Fitting	C₇×#12310	C₂
socle	C₂×C₇	C₂×#1619
hypercenter	#12310	D₇
hypocenter	C₇	C₂×#12310
LCS	G ▷ C₄×C₇×C₈ ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #12310

2180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 112

Conjugacy classes & character table

170 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.