Finite Group Databasebeta

← Prev (#37567608) Next (#37567610) →

D37×D165 #37567609

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

Aliases

direct productD37×D165
unambiguous semidirect product(C3×D37)⋊D55
unambiguous semidirect product(C5×D37)⋊D33
unambiguous semidirect product(C11×D37)⋊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 ⋊ C2×D33
HallC3×C5×C11 ⋊ C2×D37
HallC3×C37 ⋊ C2×D55
HallC5×C11 ⋊ D3×D37
SylowC37 ⋊ C2×D165
HallC3×C11 ⋊ D5×D37
HallC3×C5 ⋊ D11×D37
SylowC11 ⋊ D15×D37
SylowC5 ⋊ D33×D37
SylowC3 ⋊ D37×D55

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

1680 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 130);