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C3×C5×D1067 #44544957

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

Aliases

direct productC3×C5×D1067

Splittings

Fitting, socle, HallC3×C5×C11×C97 ⋊ C2
derived, HallC11×C97 ⋊ C2×C3×C5
HallC5×C11×C97 ⋊ C2×C3
HallC3×C11×C97 ⋊ C2×C5
HallC3×C5×C97 ⋊ D11
HallC5×C97 ⋊ C3×D11
HallC3×C97 ⋊ C5×D11
HallC3×C5×C11 ⋊ D97
SylowC97 ⋊ C3×C5×D11
HallC5×C11 ⋊ C3×D97
HallC3×C11 ⋊ C5×D97
SylowC11 ⋊ C3×C5×D97

Subgroups

subgroupG/H
center, hypercenterC3×C5D1067
commutator, cosocle, hypocenterC11×C97C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C97C2
LCSG ▷ C11×C97
UCSC1 ◁ C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16005

Conjugacy classes & character table

8025 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32010, 7);