Finite Group Databasebeta

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C17×D1023 #46852032

order34782
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D1023
unambiguous semidirect productC3⋊(C17×D341)
unambiguous semidirect productC11⋊(C17×D93)
unambiguous semidirect productC31⋊(C17×D33)

Splittings

Fitting, socle, HallC3×C11×C17×C31 ⋊ C2
derived, HallC3×C11×C31 ⋊ C2×C17
HallC11×C17×C31 ⋊ D3
HallC3×C17×C31 ⋊ D11
HallC3×C11×C17 ⋊ D31
HallC17×C31 ⋊ D33
HallC11×C31 ⋊ D3×C17
HallC11×C17 ⋊ D93
HallC3×C31 ⋊ C17×D11
HallC3×C17 ⋊ D341
HallC3×C11 ⋊ C17×D31
SylowC31 ⋊ C17×D33
SylowC11 ⋊ C17×D93
SylowC3 ⋊ C17×D341

Subgroups

subgroupG/H
center, hypercenterC17D1023
commutator, cosocle, hypocenterC3×C11×C31C2×C17
FrattiniC1G
Fitting, socleC3×C11×C17×C31C2
LCSG ▷ C3×C11×C31
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17391

Conjugacy classes & character table

8721 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34782, 15);