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C2×C17×D181⋊C3 #49147353

order36924
automorphism?
homologyAbelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C17×D181⋊C3
unambiguous semidirect productD181⋊(C2×C3×C17)
unambiguous semidirect product(C181⋊C3)⋊(C22×C17)
unambiguous semidirect product(C2×D181)⋊(C3×C17)
unambiguous semidirect product(C2×C181⋊C3)⋊(C2×C17)
unambiguous semidirect product(C2×C17×D181)⋊C3

Splittings

Fitting, socleC2×C17×C181 ⋊ C2×C3
derived, SylowC181 ⋊ C22×C3×C17
HallC2×C17×D181 ⋊ C3
HallC17×C181⋊C3 ⋊ C22
HallC17×C181 ⋊ C22×C3
HallC2×D181 ⋊ C3×C17
HallC181⋊C3 ⋊ C22×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17D181⋊C3
commutator, cosocle, hypocenterC181C22×C3×C17
FrattiniC1G
Fitting, socleC2×C17×C181C2×C3
LCSG ▷ C181
UCSC1 ◁ C2×C17

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6154

Conjugacy classes & character table

1224 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36924, 21);