Finite Group Databasebeta

#261×#478 #16800217

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct product#261×#478

Splittings

FittingC13×#478 ⋊ C4
SylowC13 ⋊ C4×#478

Subgroups

subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#478C4
socleC22×C13C2×C4×D4
prime radicalC2×D4×D13C23
cosocleC2×C4×D13C24
hypercenter#478#261
hypocenterC13C4×#478
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #478

948 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

133 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1106866);