Finite Group Databasebeta

C2×#13116602 #16015919

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13116602

Splittings

SylowC13 ⋊ C2×#2153

Subgroups

subgroupG/H
centerC2×C8C2×D52
commutatorC4×C13C23×C8
FrattiniC2×C8C23×D13
FittingC2×C13×#405C2
socleC22×C13C2×C4⋊C8
prime radicalC24×C13M16
cosocleC2×C8×C13C24
hypercenterC2×#405D13
hypocenterC13C2×#2153
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C23×C8 ◁ C2×#405

698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322568);