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C2×2−1+4×#261 #16809636

order3328
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×2−1+4×#261
unambiguous semidirect productD13⋊(C4×2−1+4)

Splittings

FittingC2×C13×2−1+4 ⋊ C4
SylowC13 ⋊ C2×C4×2−1+4

Subgroups

subgroupG/H
centerC22C24×#261
commutatorC2×C13C25×C4
FrattiniC2C25×#261
FittingC2×C13×2−1+4C4
socleC22×C13C24×C4
prime radicalC2×D13×2−1+4C2
cosocleC2×D13C26
hypercenterC2×2−1+4#261
hypocenterC13C2×C4×2−1+4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×2−1+4

11210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

238 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1116285);