Finite Group Databasebeta

#41×#6122 #16808559

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct product#41×#6122

Splittings

SylowC13 ⋊ M16×#41

Subgroups

subgroupG/H
centerC2×C4C23×#261
commutator, socleC22×C13C24×C4
FrattiniC22C24×#261
Fitting, prime radicalC22×C13×#41C4
cosocleC2×Dic13C25
hypercenterC22×#41#261
hypocenterC13M16×#41
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×#41

2232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1115208);