Finite Group Databasebeta

#261×#456 #16799812

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#261×#456

Splittings

FittingC13×#456 ⋊ C4
SylowC13 ⋊ C4×#456

Subgroups

subgroupG/H
centerC2#120×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#456C4
socleC2×C13C4×#120
prime radicalD13×2−1+4C22
cosocleC2×C4×D13C24
hypercenter#456#261
hypocenterC13C4×#456
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

1358 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1106461);