Finite Group Databasebeta

#41×#6104 #16744320

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct product#41×#6104

Splittings

FittingD4×C13×#41 ⋊ C2
SylowC13 ⋊ D8×#41

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingD4×C13×#41C2
socleC22×C13C23×D4
hypercenterD4×#41D13
hypocenterC13D8×#41
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ D4×#41

2406 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1050969);