Finite Group Databasebeta

← Prev (#37567521) Next (#37567523) →

C2×C11⋊C5×D37⋊C3 #37567522

order24420
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11⋊C5×D37⋊C3
unambiguous semidirect productD37⋊(C2×C3×C11⋊C5)
unambiguous semidirect product(C37⋊C3)⋊(C22×C11⋊C5)
unambiguous semidirect product(C2×D37)⋊(C3×C11⋊C5)
unambiguous semidirect product(C2×C37⋊C3)⋊(C2×C11⋊C5)
unambiguous semidirect product(C2×C11×D37⋊C3)⋊C5
unambiguous semidirect product(C2×C11⋊C5×D37)⋊C3

Splittings

Fitting, socleC2×C11×C37 ⋊ C2×C3×C5
derived, HallC11×C37 ⋊ C22×C3×C5
HallC2×C11⋊C5×D37 ⋊ C3
HallC11⋊C5×C37⋊C3 ⋊ C22
HallC2×C11×D37⋊C3 ⋊ C5
HallC37×C11⋊C5 ⋊ C22×C3
HallC2×C11×D37 ⋊ C3×C5
HallC11×C37⋊C3 ⋊ C22×C5
HallC2×D37 ⋊ C3×C11⋊C5
HallC37⋊C3 ⋊ C22×C11⋊C5
SylowC37 ⋊ C22×C3×C11⋊C5
SylowC11 ⋊ C2×C5×D37⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×D37⋊C3
commutator, cosocle, hypocenterC11×C37C22×C3×C5
FrattiniC1G
Fitting, socleC2×C11×C37C2×C3×C5
LCSG ▷ C11×C37
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 814

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 43);