Finite Group Databasebeta

#120×#1055 #15868415

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct product#120×#1055

Splittings

SylowC13 ⋊ C8×#120

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D13
commutatorC22×C13C23×C8
FittingC4×C13×#120C2
socleC23×C13C23×C4
prime radicalC2×C13×#120C4
cosocleC22×C4×C13C24
hypercenterC4×#120D13
hypocenterC13C8×#120
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C4×#120

1786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

448 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 175064);