Finite Group Databasebeta

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C7×D2343 #45659022

order32802
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D2343
unambiguous semidirect productC3⋊(C7×D781)
unambiguous semidirect productC11⋊(C7×D213)

Splittings

Fitting, socle, HallC3×C7×C11×C71 ⋊ C2
derived, HallC3×C11×C71 ⋊ C2×C7
HallC7×C11×C71 ⋊ D3
HallC3×C7×C71 ⋊ D11
HallC11×C71 ⋊ D3×C7
HallC7×C71 ⋊ D33
HallC3×C7×C11 ⋊ D71
HallC3×C71 ⋊ C7×D11
HallC7×C11 ⋊ D213
SylowC71 ⋊ C7×D33
HallC3×C11 ⋊ C7×D71
HallC3×C7 ⋊ D781
SylowC11 ⋊ C7×D213
SylowC3 ⋊ C7×D781

Subgroups

subgroupG/H
center, hypercenterC7D2343
commutator, cosocle, hypocenterC3×C11×C71C2×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C71C2
LCSG ▷ C3×C11×C71
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16401

Conjugacy classes & character table

8211 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32802, 14);