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C13×Dic31⋊C5 #22548977

order8060
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×Dic31⋊C5
unambiguous semidirect productDic31⋊(C5×C13)
unambiguous semidirect productΓL(1,𝔽32)⋊(C4×C13)
unambiguous semidirect product(C13×Dic31)⋊C5

Splittings

derived, SylowC31 ⋊ C4×C5×C13
HallC13×ΓL(1,𝔽32) ⋊ C4
HallC13×Dic31 ⋊ C5
HallC13×C31 ⋊ C4×C5
HallΓL(1,𝔽32) ⋊ C4×C13
HallDic31 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13D31⋊C5
commutator, hypocenterC31C4×C5×C13
FrattiniC2C13×D31⋊C5
Fitting, socleC2×C13×C31C2×C5
LCSG ▷ C31
UCSC1 ◁ C2×C13

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

338 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C13×Dic31⋊C5, C13×C3⋊(Dic31⋊C5), C13×((C31⋊C3)⋊C4)⋊C5, …
maximal normal subgroup ofC3×C13×Dic31⋊C5, C13×((C31⋊C3)⋊C4)⋊C5, C13⋊C3×Dic31⋊C5, …
maximal quotient ofC3×C13×Dic31⋊C5, C13×C3⋊(Dic31⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8060, 10);