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D13×#465 #13124392

order1664
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD13×#465

Splittings

FittingC13×#465 ⋊ C2
SylowC13 ⋊ C2×#465

Subgroups

subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#465C2
socleC22×C13C22×D4
prime radicalD13×#121C2
hypercenter#465D13
hypocenterC13C2×#465
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D13×#465, D13×#3050, D13×#3055, …
maximal normal subgroup ofC2×D13×#465, D13×#3050, D13×#3055, …
maximal quotient ofD13×#1665, D13×#1671, D13×#1677, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 14066);