Finite Group Databasebeta

C2×#41×#1055 #16727353

order3328
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC2×#41×#1055

Splittings

SylowC13 ⋊ C2×C8×#41

Subgroups

subgroupG/H
centerC2×C42C22×D13
commutatorC2×C13C24×C8
FrattiniC2×C4C24×D13
FittingC2×C4×C13×#41C2
socleC23×C13C23×C4
prime radicalC22×C13×#41C4
cosocleC2×C4×C13C25
hypercenterC2×C4×#41D13
hypocenterC13C2×C8×#41
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C2×C4×#41

2566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1034002);