Finite Group Databasebeta

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C5×A4×C23⋊C11 #29503259

order15180
automorphism?
homologyAbelianization (H1) = C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC5×A4×C23⋊C11
unambiguous semidirect productC22⋊(C3×C5×C23⋊C11)
unambiguous semidirect product(C22×C5)⋊(C3×C23⋊C11)
unambiguous semidirect productC23⋊(C5×C11×A4)
unambiguous semidirect product(C5×C23)⋊(C11×A4)
unambiguous semidirect product(A4×C23)⋊(C5×C11)
unambiguous semidirect product(C22×C23⋊C11)⋊(C3×C5)
unambiguous semidirect product(C5×A4×C23)⋊C11
unambiguous semidirect product(C22×C5×C23⋊C11)⋊C3

Splittings

Fitting, socle, HallC22×C5×C23 ⋊ C3×C11
derived, HallC22×C23 ⋊ C3×C5×C11
HallC22×C5×C23⋊C11 ⋊ C3
HallC5×A4×C23 ⋊ C11
HallC22×C23⋊C11 ⋊ C3×C5
HallA4×C23 ⋊ C5×C11
HallC5×C23 ⋊ C11×A4
SylowC23 ⋊ C5×C11×A4
HallC22×C5 ⋊ C3×C23⋊C11
SylowC22 ⋊ C3×C5×C23⋊C11

Subgroups

subgroupG/H
center, hypercenterC5A4×C23⋊C11
commutator, cosocle, hypocenterC22×C23C3×C5×C11
FrattiniC1G
Fitting, socleC22×C5×C23C3×C11
LCSG ▷ C22×C23
UCSC1 ◁ C5

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 460

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 45);