Finite Group Databasebeta

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C31×D561 #46852033

order34782
automorphism?
homologyAbelianization (H1) = C2×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×D561
unambiguous semidirect productC3⋊(C31×D187)
unambiguous semidirect productC11⋊(C31×D51)
unambiguous semidirect productC17⋊(C31×D33)

Splittings

Fitting, socle, HallC3×C11×C17×C31 ⋊ C2
derived, HallC3×C11×C17 ⋊ C2×C31
HallC11×C17×C31 ⋊ D3
HallC3×C17×C31 ⋊ D11
HallC3×C11×C31 ⋊ D17
HallC17×C31 ⋊ D33
HallC11×C31 ⋊ D51
HallC11×C17 ⋊ D3×C31
HallC3×C31 ⋊ D187
HallC3×C17 ⋊ D11×C31
HallC3×C11 ⋊ C31×D17
SylowC17 ⋊ C31×D33
SylowC11 ⋊ C31×D51
SylowC3 ⋊ C31×D187

Subgroups

subgroupG/H
center, hypercenterC31D561
commutator, cosocle, hypocenterC3×C11×C17C2×C31
FrattiniC1G
Fitting, socleC3×C11×C17×C31C2
LCSG ▷ C3×C11×C17
UCSC1 ◁ C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17391

Conjugacy classes & character table

8742 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34782, 16);