Finite Group Databasebeta

C2×#13116521 #16015749

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13116521

Splittings

SylowC13 ⋊ C2×#2132

Subgroups

subgroupG/H
centerC2×C4#88074
commutatorC2×C4×C13C23×C4
FrattiniC2×Q8C23×D13
Fitting, prime radicalC2×C13×#532C2
socleC22×C13C2×#99
cosocleC2×Q8×C13C24
hypercenterC2×#532D13
hypocenterC13C2×#2132
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#532

1306 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322398);