Finite Group Databasebeta

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C22×C3×C13×C29⋊C7 #44539882

order31668
automorphism?
homologyAbelianization (H1) = C22×C3×C7×C13 · Schur multiplier (H2) = C2

Aliases

direct productC22×C3×C13×C29⋊C7
unambiguous semidirect product(C22×C3×C29)⋊(C7×C13)
unambiguous semidirect product(C22×C3×C13×C29)⋊C7

Splittings

Fitting, socle, HallC22×C3×C13×C29 ⋊ C7
derived, SylowC29 ⋊ C22×C3×C7×C13
HallC22×C13×C29 ⋊ C3×C7
HallC3×C13×C29 ⋊ C22×C7
HallC13×C29 ⋊ C22×C3×C7
HallC22×C3×C29 ⋊ C7×C13
HallC22×C29 ⋊ C3×C7×C13
HallC3×C29 ⋊ C22×C7×C13

Subgroups

subgroupG/H
center, hypercenterC22×C3×C13C29⋊C7
commutator, cosocle, hypocenterC29C22×C3×C7×C13
FrattiniC1G
Fitting, socleC22×C3×C13×C29C7
LCSG ▷ C29
UCSC1 ◁ C22×C3×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4524

Conjugacy classes & character table

1716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 177);