Finite Group Databasebeta

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D₇×#23900 #72259459

order	3584
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹²

Aliases

Splittings

Fitting	C₇×#23900 ⋊ C₂
Sylow	C₇ ⋊ C₂×#23900

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₇×#120
commutator, cosocle	C₂⁴×C₇	C₂⁵
Frattini	C₂⁴	C₂⁴×D₇
Fitting	C₇×#23900	C₂
socle	C₂²×C₇	C₂²×#120
hypercenter	#23900	D₇
hypocenter	C₇	C₂×#23900
LCS	G ▷ C₂⁴×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ #23900

29984 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	AGL(1,𝔽₇)×#23900
maximal normal subgroup of	AGL(1,𝔽₇)×#23900

GAP

Past the SmallGroups library coverage — no SmallGroups id.