Finite Group Databasebeta

← Prev (#72259762) Next (#72259764) →

D₇×#11992 #72259763

order	3584
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

Splittings

Fitting	C₇×#11992 ⋊ C₂
Sylow	C₇ ⋊ C₂×#11992

Subgroups

	subgroup	G/H
center	C₂	D₇×#1555
commutator	C₄²×C₇	C₂³×C₄
Frattini	C₄×C₈	C₂³×D₇
Fitting	C₇×#11992	C₂
socle	C₂×C₇	C₂×#1555
prime radical	D₇×#3151	C₂
cosocle	C₄×C₇×C₈	C₂⁴
hypercenter	#11992	D₇
hypocenter	C₇	C₂×#11992
LCS	G ▷ C₄²×C₇ ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #11992

2348 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 112

Conjugacy classes & character table

140 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.