Finite Group Databasebeta

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C2×C3×C37×D55 #37567638

order24420
automorphism?
homologyAbelianization (H1) = C22×C3×C37 · Schur multiplier (H2) = C2

Aliases

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

Splittings

Fitting, socleC2×C3×C5×C11×C37 ⋊ C2
derived, HallC5×C11 ⋊ C22×C3×C37
HallC3×C5×C11×C37 ⋊ C22
HallC5×C11×C37 ⋊ C22×C3
HallC3×C11×C37 ⋊ C2×D5
HallC3×C5×C37 ⋊ C2×D11
HallC11×C37 ⋊ C2×C3×D5
HallC5×C37 ⋊ C2×C3×D11
HallC3×C5×C11 ⋊ C22×C37
HallC3×C11 ⋊ C2×D5×C37
HallC3×C5 ⋊ C2×D11×C37
SylowC11 ⋊ C2×C3×D5×C37
SylowC5 ⋊ C2×C3×D11×C37

Subgroups

subgroupG/H
center, hypercenterC2×C3×C37D55
commutator, cosocle, hypocenterC5×C11C22×C3×C37
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C37C2
LCSG ▷ C5×C11
UCSC1 ◁ C2×C3×C37

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12210

Conjugacy classes & character table

6438 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 159);