Finite Group Databasebeta

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C22×C32×C5×C29⋊C7 #49141499

order36540
automorphism?
homologyAbelianization (H1) = C22×C32×C5×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC22×C32×C5×C29⋊C7
unambiguous semidirect product(C22×C32×C29)⋊(C5×C7)
unambiguous semidirect product(C22×C32×C5×C29)⋊C7

Splittings

Fitting, socle, HallC22×C32×C5×C29 ⋊ C7
derived, SylowC29 ⋊ C22×C32×C5×C7
HallC32×C5×C29 ⋊ C22×C7
HallC22×C32×C29 ⋊ C5×C7
HallC22×C5×C29 ⋊ C32×C7
HallC32×C29 ⋊ C22×C5×C7
HallC5×C29 ⋊ C22×C32×C7
HallC22×C29 ⋊ C32×C5×C7

Subgroups

subgroupG/H
center, hypercenterC22×C32×C5C29⋊C7
commutator, cosocle, hypocenterC29C22×C32×C5×C7
FrattiniC1G
Fitting, socleC22×C32×C5×C29C7
LCSG ▷ C29
UCSC1 ◁ C22×C32×C5

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5220

Conjugacy classes & character table

1980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 341);