Finite Group Databasebeta

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C2×C5×C11×D37⋊C3 #37567563

order24420
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

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

Splittings

Fitting, socleC2×C5×C11×C37 ⋊ C2×C3
derived, SylowC37 ⋊ C22×C3×C5×C11
HallC2×C5×C11×D37 ⋊ C3
HallC5×C11×C37⋊C3 ⋊ C22
HallC5×C11×C37 ⋊ C22×C3
HallC2×C11×D37 ⋊ C3×C5
HallC11×C37⋊C3 ⋊ C22×C5
HallC2×C5×D37 ⋊ C3×C11
HallC5×C37⋊C3 ⋊ C22×C11
HallC11×C37 ⋊ C22×C3×C5
HallC5×C37 ⋊ C22×C3×C11
HallC2×D37 ⋊ C3×C5×C11
HallC37⋊C3 ⋊ C22×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D37⋊C3
commutator, cosocle, hypocenterC37C22×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C5×C11×C37C2×C3
LCSG ▷ C37
UCSC1 ◁ C2×C5×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4070

Conjugacy classes & character table

1320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 84);