Finite Group Databasebeta

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C2×C17×D163⋊C3 #45685276

order33252
automorphism?
homologyAbelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C17×D163⋊C3
unambiguous semidirect productD163⋊(C2×C3×C17)
unambiguous semidirect product(C163⋊C3)⋊(C22×C17)
unambiguous semidirect product(C2×D163)⋊(C3×C17)
unambiguous semidirect product(C2×C163⋊C3)⋊(C2×C17)
unambiguous semidirect product(C2×C17×D163)⋊C3

Splittings

Fitting, socleC2×C17×C163 ⋊ C2×C3
derived, SylowC163 ⋊ C22×C3×C17
HallC2×C17×D163 ⋊ C3
HallC17×C163⋊C3 ⋊ C22
HallC17×C163 ⋊ C22×C3
HallC2×D163 ⋊ C3×C17
HallC163⋊C3 ⋊ C22×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17D163⋊C3
commutator, cosocle, hypocenterC163C22×C3×C17
FrattiniC1G
Fitting, socleC2×C17×C163C2×C3
LCSG ▷ C163
UCSC1 ◁ C2×C17

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5542

Conjugacy classes & character table

1122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33252, 17);