Finite Group Databasebeta

C2×#13129659 #16778908

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C42

Aliases

direct productC2×#13129659

Splittings

FittingC2×C4×C8×C13 ⋊ C4
SylowC13 ⋊ C2×#1274

Subgroups

subgroupG/H
centerC22×C4C4×#261
commutatorC4×C13C2×C4×C8
FrattiniC42C22×#261
FittingC2×C4×C8×C13C4
socleC23×C13#95
prime radicalC23×D13C22⋊C4
cosocleC42×D13C23
hypercenterC2×C4×C8#261
hypocenterC13C2×#1274
LCSG ▷ C4×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×C8

758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1085557);