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C32×D1015 #32912540

order18270
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC32×D1015
unambiguous semidirect productC5⋊(C32×D203)
unambiguous semidirect productC29⋊(C32×D35)

Splittings

Fitting, socle, HallC32×C5×C7×C29 ⋊ C2
derived, HallC5×C7×C29 ⋊ C2×C32
HallC32×C7×C29 ⋊ D5
HallC32×C5×C29 ⋊ D7
HallC32×C5×C7 ⋊ D29
HallC32×C29 ⋊ D35
HallC7×C29 ⋊ C32×D5
HallC5×C29 ⋊ C32×D7
HallC32×C7 ⋊ D145
HallC32×C5 ⋊ D203
HallC5×C7 ⋊ C32×D29
SylowC29 ⋊ C32×D35
SylowC7 ⋊ C32×D145
SylowC5 ⋊ C32×D203

Subgroups

subgroupG/H
center, hypercenterC32D1015
commutator, cosocle, hypocenterC5×C7×C29C2×C32
FrattiniC1G
Fitting, socleC32×C5×C7×C29C2
LCSG ▷ C5×C7×C29
UCSC1 ◁ C32

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

4581 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×D29×D35, C32×D7×D145, C32×D5×D203, …
maximal normal subgroup ofC32×D29×D35, C32×D7×D145, C32×D5×D203, …
maximal quotient ofC32×Dic1015, C2×C32×D1015

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 78);