Finite Group Databasebeta

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A4×C37×C11⋊C5 #37567534

order24420
automorphism?
homologyAbelianization (H1) = C3×C5×C37 · Schur multiplier (H2) = C2

Aliases

direct productA4×C37×C11⋊C5
unambiguous semidirect productC22⋊(C3×C37×C11⋊C5)
unambiguous semidirect productC11⋊(C5×A4×C37)
unambiguous semidirect product(C11×A4)⋊(C5×C37)
unambiguous semidirect product(C22×C11⋊C5)⋊(C3×C37)
unambiguous semidirect product(C11×A4×C37)⋊C5

Splittings

Fitting, socle, HallC22×C11×C37 ⋊ C3×C5
derived, HallC22×C11 ⋊ C3×C5×C37
HallC22×C37×C11⋊C5 ⋊ C3
HallC11×A4×C37 ⋊ C5
HallC11×C37 ⋊ C5×A4
HallC22×C11⋊C5 ⋊ C3×C37
HallC22×C37 ⋊ C3×C11⋊C5
HallC11×A4 ⋊ C5×C37
SylowC11 ⋊ C5×A4×C37
SylowC22 ⋊ C3×C37×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC37A4×C11⋊C5
commutator, cosocle, hypocenterC22×C11C3×C5×C37
FrattiniC1G
Fitting, socleC22×C11×C37C3×C5
LCSG ▷ C22×C11
UCSC1 ◁ C37

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1628

Conjugacy classes & character table

1036 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 55);