Finite Group Databasebeta

#41×Dic52 #16744392

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct product#41×Dic52

Splittings

SylowC13 ⋊ Q16×#41

Subgroups

subgroupG/H
centerC2×C4C22×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC8×C13×#41C2
socleC22×C13C23×D4
prime radicalC2×C13×#41D4
hypercenterC8×#41D13
hypocenterC13Q16×#41
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C8×#41

1826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1051041);