Finite Group Databasebeta

C2×#13112761 #15771987

order3328
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#13112761

Splittings

FittingC2×C13×C22⋊C16 ⋊ C2
SylowC13 ⋊ C2×#1315

Subgroups

subgroupG/H
centerC22×C4#6103
commutatorC2×C4×C13C22×C8
FrattiniC22×C8C22×D13
FittingC2×C13×C22⋊C16C2
socleC23×C13C22⋊C8
prime radicalC22×#6127C4
cosocleC22×C8×C13C23
hypercenterC2×C22⋊C16D13
hypocenterC13C2×#1315
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C2×C22⋊C16

534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 78636);