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C13×ΓL(1,𝔽32)⋊C9 #31827440

order18135
automorphism?
homologyAbelianization (H1) = C5×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×ΓL(1,𝔽32)⋊C9
unambiguous semidirect productΓL(1,𝔽32)⋊(C9×C13)
unambiguous semidirect product(C31⋊C9)⋊(C5×C13)
unambiguous semidirect product(C13×C31⋊C9)⋊C5

Splittings

derived, SylowC31 ⋊ C5×C9×C13
HallC13×C31⋊C9 ⋊ C5
HallC13×ΓL(1,𝔽32) ⋊ C9
HallC13×C31 ⋊ C5×C9
HallC31⋊C9 ⋊ C5×C13
HallΓL(1,𝔽32) ⋊ C9×C13

Subgroups

subgroupG/H
center, hypercenterC3×C13(C31⋊C3)⋊C5
commutator, hypocenterC31C5×C9×C13
FrattiniC3C13×(C31⋊C3)⋊C5
Fitting, socleC3×C13×C31C3×C5
prime radicalC3×C13×ΓL(1,𝔽32)C3
cosocleC3×C31C3×C5×C13
LCSG ▷ C31
UCSC1 ◁ C3×C13

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3627

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C13×ΓL(1,𝔽32)⋊C9, C13×(D31⋊C5)⋊C9, D13×ΓL(1,𝔽32)⋊C9, …
maximal normal subgroup ofC2×C13×ΓL(1,𝔽32)⋊C9, C13×(D31⋊C5)⋊C9, D13×ΓL(1,𝔽32)⋊C9, …
maximal quotient ofC2×C13×ΓL(1,𝔽32)⋊C9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18135, 7);