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C2×C13⋊(D31⋊C5) #22548985

order8060
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13⋊(D31⋊C5)
unambiguous semidirect product(C2×C13)⋊(D31⋊C5)
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊D13
unambiguous semidirect product(C2×D403)⋊C5

Splittings

Fitting, socleC2×C13×C31 ⋊ C2×C5
derived, HallC13×C31 ⋊ C22×C5
HallC13×ΓL(1,𝔽32) ⋊ C22
HallC2×D403 ⋊ C5
HallΓL(1,𝔽32) ⋊ C2×D13
SylowC31 ⋊ C2×C5×D13
SylowC13 ⋊ C2×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C13⋊(D31⋊C5)
commutator, hypocenterC13×C31C22×C5
FrattiniC1G
Fitting, socleC2×C13×C31C2×C5
LCSG ▷ C13×C31
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

158 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#14559031⋊C5, C2×#14559030⋊C5, C2×(C13⋊C3)⋊(D31⋊C5), …
maximal normal subgroup ofC2×#14559031⋊C5, C2×#14559030⋊C5, C2×(C13⋊C3)⋊(D31⋊C5), …
maximal quotient ofD3×C13⋊(D31⋊C5), C2×C3×C13⋊(D31⋊C5), C2×C3⋊(C13⋊(D31⋊C5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8060, 18);