Finite Group Databasebeta

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C5×D3×C11×D37 #37567591

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

Aliases

direct productC5×D3×C11×D37
unambiguous semidirect product(D3×C37)⋊(C2×C5×C11)
unambiguous semidirect product(C3×D37)⋊(C2×C5×C11)
unambiguous semidirect productD111⋊(C2×C5×C11)

Splittings

Fitting, socle, HallC3×C5×C11×C37 ⋊ C22
derived, HallC3×C37 ⋊ C22×C5×C11
HallC5×C11×C37 ⋊ C2×D3
HallC3×C11×C37 ⋊ C22×C5
HallC3×C5×C37 ⋊ C22×C11
HallC11×C37 ⋊ C2×C5×D3
HallC5×C37 ⋊ C2×D3×C11
HallC3×C5×C11 ⋊ C2×D37
SylowC37 ⋊ C2×C5×D3×C11
HallC3×C11 ⋊ C2×C5×D37
HallC3×C5 ⋊ C2×C11×D37
SylowC3 ⋊ C2×C5×C11×D37

Subgroups

subgroupG/H
center, hypercenterC5×C11D3×D37
commutator, cosocle, hypocenterC3×C37C22×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C37C22
LCSG ▷ C3×C37
UCSC1 ◁ C5×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6105

Conjugacy classes & character table

3300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 112);