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C32×D1001 #31825093

order18018
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC32×D1001
unambiguous semidirect productC11⋊(C32×D91)

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C2
derived, HallC7×C11×C13 ⋊ C2×C32
HallC32×C11×C13 ⋊ D7
HallC32×C7×C13 ⋊ D11
HallC32×C7×C11 ⋊ D13
HallC11×C13 ⋊ C32×D7
HallC32×C13 ⋊ D77
HallC32×C11 ⋊ D91
HallC7×C13 ⋊ C32×D11
HallC7×C11 ⋊ C32×D13
HallC32×C7 ⋊ D143
SylowC13 ⋊ C32×D77
SylowC11 ⋊ C32×D91
SylowC7 ⋊ C32×D143

Subgroups

subgroupG/H
center, hypercenterC32D1001
commutator, cosocle, hypocenterC7×C11×C13C2×C32
FrattiniC1G
Fitting, socleC32×C7×C11×C13C2
LCSG ▷ C7×C11×C13
UCSC1 ◁ C32

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9009

Conjugacy classes & character table

4518 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×D13×D77, C32×D11×D91, C32×D7×D143, …
maximal normal subgroup ofC32×D13×D77, C32×D11×D91, C32×D7×D143, …
maximal quotient ofC32×Dic1001, C2×C32×D1001

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18018, 138);