Finite Group Databasebeta

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C22×C11⋊C5×C43⋊C3 #43248804

order28380
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC22×C11⋊C5×C43⋊C3
unambiguous semidirect product(C22×C11×C43⋊C3)⋊C5

Splittings

Fitting, socle, HallC22×C11×C43 ⋊ C3×C5
derived, HallC11×C43 ⋊ C22×C3×C5
HallC22×C43×C11⋊C5 ⋊ C3
HallC22×C11×C43⋊C3 ⋊ C5
HallC43×C11⋊C5 ⋊ C22×C3
HallC11×C43⋊C3 ⋊ C22×C5
HallC22×C43 ⋊ C3×C11⋊C5
HallC22×C11 ⋊ C5×C43⋊C3
SylowC43 ⋊ C22×C3×C11⋊C5
SylowC11 ⋊ C22×C5×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC22C11⋊C5×C43⋊C3
commutator, cosocle, hypocenterC11×C43C22×C3×C5
FrattiniC1G
Fitting, socleC22×C11×C43C3×C5
LCSG ▷ C11×C43
UCSC1 ◁ C22

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1892

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28380, 51);