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C5×D11×C97⋊C3 #44544978

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

Aliases

direct productC5×D11×C97⋊C3
unambiguous semidirect product(C5×D11×C97)⋊C3

Splittings

Fitting, socle, HallC5×C11×C97 ⋊ C2×C3
derived, HallC11×C97 ⋊ C2×C3×C5
HallC5×C11×C97⋊C3 ⋊ C2
HallC5×D11×C97 ⋊ C3
HallC11×C97⋊C3 ⋊ C2×C5
HallD11×C97 ⋊ C3×C5
HallC5×C97 ⋊ C3×D11
SylowC97 ⋊ C3×C5×D11
HallC5×C11 ⋊ C2×C97⋊C3
SylowC11 ⋊ C2×C5×C97⋊C3

Subgroups

subgroupG/H
center, hypercenterC5D11×C97⋊C3
commutator, cosocle, hypocenterC11×C97C2×C3×C5
FrattiniC1G
Fitting, socleC5×C11×C97C2×C3
LCSG ▷ C11×C97
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5335

Conjugacy classes & character table

1225 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32010, 28);