Finite Group Databasebeta

C2×#13116523 #16015752

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

Aliases

direct productC2×#13116523

Splittings

FittingC22×C13×#101 ⋊ C2
SylowC13 ⋊ C2×#2133

Subgroups

subgroupG/H
centerC22C2×#88046
commutatorC2×C4×C13C23×C4
FrattiniC2×Q8C23×D13
FittingC22×C13×#101C2
socleC22×C13C2×#99
prime radicalC22×#6127C4
cosocleC2×Q8×C13C24
hypercenterC22×#101D13
hypocenterC13C2×#2133
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×Q8 ◁ C22×#101

1198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322401);