Finite Group Databasebeta

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C22×C3×C29×C11⋊C5 #34062352

order19140
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C29 · Schur multiplier (H2) = C2

Aliases

direct productC22×C3×C29×C11⋊C5
unambiguous semidirect product(C22×C3×C11)⋊(C5×C29)
unambiguous semidirect product(C22×C3×C11×C29)⋊C5

Splittings

Fitting, socle, HallC22×C3×C11×C29 ⋊ C5
derived, SylowC11 ⋊ C22×C3×C5×C29
HallC22×C11×C29 ⋊ C3×C5
HallC3×C11×C29 ⋊ C22×C5
HallC11×C29 ⋊ C22×C3×C5
HallC22×C3×C11 ⋊ C5×C29
HallC22×C11 ⋊ C3×C5×C29
HallC3×C11 ⋊ C22×C5×C29

Subgroups

subgroupG/H
center, hypercenterC22×C3×C29C11⋊C5
commutator, cosocle, hypocenterC11C22×C3×C5×C29
FrattiniC1G
Fitting, socleC22×C3×C11×C29C5
LCSG ▷ C11
UCSC1 ◁ C22×C3×C29

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3828

Conjugacy classes & character table

2436 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 45);