Finite Group Databasebeta

#41×C22⋊#261 #16807564

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct product#41×C22⋊#261

Splittings

FittingC22×C13×#41 ⋊ C4
SylowC13 ⋊ C22⋊C4×#41

Subgroups

subgroupG/H
centerC2×C4C23×#261
commutator, socleC22×C13C24×C4
FrattiniC22C24×#261
FittingC22×C13×#41C4
prime radicalC22×#41×D13C2
cosocleC22×D13C25
hypercenterC22×#41#261
hypocenterC13C22⋊C4×#41
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×#41

5646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

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, 1114213);