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C3×D11×D185 #37567587

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

Aliases

direct productC3×D11×D185
unambiguous semidirect product(C5×D11)⋊(C3×D37)

Splittings

Fitting, socle, HallC3×C5×C11×C37 ⋊ C22
derived, 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 ⋊ C2×D37
HallC3×C37 ⋊ D5×D11
HallC5×C11 ⋊ C2×C3×D37
SylowC37 ⋊ C3×D5×D11
HallC3×C11 ⋊ C2×D185
HallC3×C5 ⋊ D11×D37
SylowC11 ⋊ C2×C3×D185
SylowC5 ⋊ C3×D11×D37

Subgroups

subgroupG/H
center, hypercenterC3D11×D185
commutator, cosocle, hypocenterC5×C11×C37C22×C3
FrattiniC1G
Fitting, socleC3×C5×C11×C37C22
LCSG ▷ C5×C11×C37
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6105

Conjugacy classes & character table

1974 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 108);