Finite Group Databasebeta

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C7×#10595278 #72246848

order4032
automorphism?
homologyAbelianization (H1) = C24×C7 · Schur multiplier (H2) = C27

Aliases

direct productC7×#10595278

Splittings

FittingC2×C32×C7×D4 ⋊ C22
HallC32×C7 ⋊ C2×#120
SylowC32 ⋊ C2×C7×#120

Subgroups

subgroupG/H
centerC22×C7C22×D32
commutator, cosocleC22×C32C24×C7
FrattiniC22C22×D32×C7
FittingC2×C32×C7×D4C22
socleC22×C32×C7C24
hypercenterC2×C7×D4D32
hypocenterC32C2×C7×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C7 ◁ C2×C7×D4

2884 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 336

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD7×#10595278
maximal normal subgroup ofD7×#10595278
maximal quotient ofC7×#11864777

GAP

Past the SmallGroups library coverage — no SmallGroups id.