Finite Group Databasebeta

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C3×C11×D527 #46852022

order34782
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D527
unambiguous semidirect productC17⋊(C3×C11×D31)

Splittings

Fitting, socle, HallC3×C11×C17×C31 ⋊ C2
derived, HallC17×C31 ⋊ C2×C3×C11
HallC11×C17×C31 ⋊ C2×C3
HallC3×C17×C31 ⋊ C2×C11
HallC3×C11×C31 ⋊ D17
HallC3×C11×C17 ⋊ D31
HallC11×C31 ⋊ C3×D17
HallC11×C17 ⋊ C3×D31
HallC3×C31 ⋊ C11×D17
HallC3×C17 ⋊ C11×D31
SylowC31 ⋊ C3×C11×D17
SylowC17 ⋊ C3×C11×D31

Subgroups

subgroupG/H
center, hypercenterC3×C11D527
commutator, cosocle, hypocenterC17×C31C2×C3×C11
FrattiniC1G
Fitting, socleC3×C11×C17×C31C2
LCSG ▷ C17×C31
UCSC1 ◁ C3×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17391

Conjugacy classes & character table

8745 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34782, 5);