Finite Group Databasebeta

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C11⋊C5×C22⋊(C37⋊C3) #37567535

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

Aliases

direct productC11⋊C5×C22⋊(C37⋊C3)
unambiguous semidirect productC22⋊(C11⋊C5×C37⋊C3)
unambiguous semidirect productC11⋊(C5×C22⋊(C37⋊C3))
unambiguous semidirect productC37⋊(A4×C11⋊C5)
unambiguous semidirect product(C22×C11⋊C5)⋊(C37⋊C3)
unambiguous semidirect product(C37×C11⋊C5)⋊A4
unambiguous semidirect product(C11×C22⋊(C37⋊C3))⋊C5

Splittings

Fitting, socle, derived, HallC22×C11×C37 ⋊ C3×C5
HallC22×C37×C11⋊C5 ⋊ C3
HallC11×C22⋊(C37⋊C3) ⋊ C5
HallC37×C11⋊C5 ⋊ A4
HallC11×C37 ⋊ C5×A4
HallC22×C11⋊C5 ⋊ C37⋊C3
HallC22×C37 ⋊ C3×C11⋊C5
HallC22×C11 ⋊ C5×C37⋊C3
SylowC37 ⋊ A4×C11⋊C5
SylowC11 ⋊ C5×C22⋊(C37⋊C3)
SylowC22 ⋊ C11⋊C5×C37⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC22×C11×C37C3×C5
LCSG ▷ C22×C11×C37
UCSC1

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1628

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 56);