Finite Group Databasebeta

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D11×D555 #37567611

order24420
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD11×D555
unambiguous semidirect product(C3×D11)⋊D185
unambiguous semidirect product(C5×D11)⋊D111
unambiguous semidirect product(D11×C37)⋊D15

Splittings

Fitting, socle, derived, HallC3×C5×C11×C37 ⋊ C22
HallC5×C11×C37 ⋊ C2×D3
HallC3×C11×C37 ⋊ C2×D5
HallC3×C5×C37 ⋊ C2×D11
HallC11×C37 ⋊ C2×D15
HallC5×C37 ⋊ D3×D11
HallC3×C5×C11 ⋊ C2×D37
HallC3×C37 ⋊ D5×D11
HallC5×C11 ⋊ C2×D111
SylowC37 ⋊ D11×D15
HallC3×C11 ⋊ C2×D185
HallC3×C5 ⋊ D11×D37
SylowC11 ⋊ C2×D555
SylowC5 ⋊ D11×D111
SylowC3 ⋊ D11×D185

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C37C22
LCSG ▷ C3×C5×C11×C37
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6105

Conjugacy classes & character table

1953 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 132);