Finite Group Databasebeta

C2×#13116520 #16015748

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

Aliases

direct productC2×#13116520

Splittings

FittingC2×C13×#356 ⋊ C2
SylowC13 ⋊ C2×#2132

Subgroups

subgroupG/H
centerC22D13×#99
commutatorC2×C4×C13C23×C4
FrattiniC2×Q8C23×D13
FittingC2×C13×#356C2
socleC22×C13C2×#99
prime radicalC2×#11719430C2
cosocleC2×Q8×C13C24
hypercenterC2×#356D13
hypocenterC13C2×#2132
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

1306 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322397);