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C22×C13×ΓL(1,𝔽32) #22548987

order8060
isoclinismisoclinic class of ΓL(1,𝔽32)
automorphism?
homologyAbelianization (H1) = C22×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC22×C13×ΓL(1,𝔽32)
unambiguous semidirect product(C22×C31)⋊(C5×C13)
unambiguous semidirect product(C22×C13×C31)⋊C5

Splittings

Fitting, socle, HallC22×C13×C31 ⋊ C5
derived, SylowC31 ⋊ C22×C5×C13
HallC13×C31 ⋊ C22×C5
HallC22×C31 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC22×C13ΓL(1,𝔽32)
commutator, hypocenterC31C22×C5×C13
FrattiniC1G
Fitting, socleC22×C13×C31C5
LCSG ▷ C31
UCSC1 ◁ C22×C13

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×C22⋊((C31⋊C3)⋊C5), A4×C13×ΓL(1,𝔽32), C22⋊(#11925881⋊C5), …
maximal normal subgroup ofC13×C22⋊((C31⋊C3)⋊C5), A4×C13×ΓL(1,𝔽32), C22⋊(#11925881⋊C5), …
maximal quotient ofC2×D3×C13×ΓL(1,𝔽32), C22×C3×C13×ΓL(1,𝔽32)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8060, 20);