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C5×C11×D97⋊C3 #44544977

order32010
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D97⋊C3
unambiguous semidirect productD97⋊(C3×C5×C11)
unambiguous semidirect product(C97⋊C3)⋊(C2×C5×C11)
unambiguous semidirect product(C5×D97)⋊(C3×C11)
unambiguous semidirect product(C5×C11×D97)⋊C3

Splittings

Fitting, socle, HallC5×C11×C97 ⋊ C2×C3
derived, SylowC97 ⋊ C2×C3×C5×C11
HallC5×C11×C97⋊C3 ⋊ C2
HallC5×C11×D97 ⋊ C3
HallC11×C97⋊C3 ⋊ C2×C5
HallC11×D97 ⋊ C3×C5
HallC5×C97⋊C3 ⋊ C2×C11
HallC11×C97 ⋊ C2×C3×C5
HallC5×D97 ⋊ C3×C11
HallC5×C97 ⋊ C2×C3×C11
HallC97⋊C3 ⋊ C2×C5×C11
HallD97 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11D97⋊C3
commutator, cosocle, hypocenterC97C2×C3×C5×C11
FrattiniC1G
Fitting, socleC5×C11×C97C2×C3
LCSG ▷ C97
UCSC1 ◁ C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5335

Conjugacy classes & character table

1210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32010, 27);