Finite Group Databasebeta

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C11×C17×D93 #46852028

order34782
automorphism?
homologyAbelianization (H1) = C2×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC11×C17×D93
unambiguous semidirect productC3⋊(C11×C17×D31)
unambiguous semidirect productC31⋊(D3×C11×C17)

Splittings

Fitting, socle, HallC3×C11×C17×C31 ⋊ C2
derived, HallC3×C31 ⋊ C2×C11×C17
HallC11×C17×C31 ⋊ D3
HallC3×C17×C31 ⋊ C2×C11
HallC3×C11×C31 ⋊ C2×C17
HallC3×C11×C17 ⋊ D31
HallC17×C31 ⋊ D3×C11
HallC11×C31 ⋊ D3×C17
HallC3×C17 ⋊ C11×D31
HallC3×C11 ⋊ C17×D31
SylowC31 ⋊ D3×C11×C17
SylowC3 ⋊ C11×C17×D31

Subgroups

subgroupG/H
center, hypercenterC11×C17D93
commutator, cosocle, hypocenterC3×C31C2×C11×C17
FrattiniC1G
Fitting, socleC3×C11×C17×C31C2
LCSG ▷ C3×C31
UCSC1 ◁ C11×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17391

Conjugacy classes & character table

8976 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34782, 11);