Finite Group Databasebeta

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C2×C3×D5×C11×C37 #37567636

order24420
automorphism?
homologyAbelianization (H1) = C22×C3×C11×C37 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D5×C11×C37
unambiguous semidirect productC5⋊(C22×C3×C11×C37)
unambiguous semidirect product(C2×C5)⋊(C2×C3×C11×C37)

Splittings

Fitting, socleC2×C3×C5×C11×C37 ⋊ C2
derived, SylowC5 ⋊ C22×C3×C11×C37
HallC3×C5×C11×C37 ⋊ C22
HallC5×C11×C37 ⋊ C22×C3
HallC3×C5×C37 ⋊ C22×C11
HallC5×C37 ⋊ C22×C3×C11
HallC3×C5×C11 ⋊ C22×C37
HallC5×C11 ⋊ C22×C3×C37
HallC3×C5 ⋊ C22×C11×C37

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11×C37D5
commutator, cosocle, hypocenterC5C22×C3×C11×C37
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C37C2
LCSG ▷ C5
UCSC1 ◁ C2×C3×C11×C37

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12210

Conjugacy classes & character table

9768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 157);