Finite Group Databasebeta

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C2×D55×C37⋊C3 #37567569

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

Aliases

direct productC2×D55×C37⋊C3
unambiguous semidirect product(C2×C5)⋊(D11×C37⋊C3)
unambiguous semidirect product(C2×C11)⋊(D5×C37⋊C3)
unambiguous semidirect product(C2×C37×D55)⋊C3

Splittings

Fitting, socleC2×C5×C11×C37 ⋊ C2×C3
derived, HallC5×C11×C37 ⋊ C22×C3
HallC2×C37×D55 ⋊ C3
HallC5×C11×C37⋊C3 ⋊ C22
HallC11×C37⋊C3 ⋊ C2×D5
HallC5×C37⋊C3 ⋊ C2×D11
HallC11×C37 ⋊ C2×C3×D5
HallC5×C37 ⋊ C2×C3×D11
HallC5×C11 ⋊ C22×C37⋊C3
SylowC37 ⋊ C2×C3×D55
SylowC11 ⋊ C2×D5×C37⋊C3
SylowC5 ⋊ C2×D11×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC2D55×C37⋊C3
commutator, cosocle, hypocenterC5×C11×C37C22×C3
FrattiniC1G
Fitting, socleC2×C5×C11×C37C2×C3
LCSG ▷ C5×C11×C37
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4070

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 90);