Finite Group Databasebeta

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C7×#89804⋊C3 #72246121

order9408
automorphism?
homologyAbelianization (H1) = C23×C3×C7 · Schur multiplier (H2) = C24

Aliases

direct productC7×#89804⋊C3

Splittings

FittingC72×#120 ⋊ C2×C3
HallC7×#89804 ⋊ C3
HallC7×ΓL(1,𝔽8) ⋊ B(4,𝔽2)
SylowC72 ⋊ C3×B(4,𝔽2)

Subgroups

subgroupG/H
centerC2×C7#6500⋊C3
commutator, cosocleC23×C7C23×C3×C7
FrattiniC23C22×C7×AGL(1,𝔽7)
FittingC72×#120C2×C3
socleC2×C72C3×#120
hypercenterC7×#120AGL(1,𝔽7)
hypocenterC7C3×C7×B(4,𝔽2)
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C7 ◁ C23×C7 ◁ C7×#120

857 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

434 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#72246128
maximal normal subgroup of#72246128

GAP

Past the SmallGroups library coverage — no SmallGroups id.