Finite Group Databasebeta

C2×#13112848 #15773142

order3328
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#13112848

Splittings

SylowC13 ⋊ C2×#1348

Subgroups

subgroupG/H
centerC23#88072
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC2×C13×#467C2
socleC23×C13#102
prime radicalC24×C13D8
cosocleC22×C8×C13C23
hypercenterC2×#467D13
hypocenterC13C2×#1348
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#467

506 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 79791);