Finite Group Databasebeta

C2×#13129751 #16786592

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×#13129751

Splittings

SylowC13 ⋊ C2×#1312

Subgroups

subgroupG/H
centerC2×C42C2×#261
commutatorC2×C13C2×C4×C16
FrattiniC42C22×#261
FittingC2×C4×C8×C13C4
socle, prime radicalC23×C13C4×C8
cosocleC4×#1055C23
hypercenterC2×C4×C8#261
hypocenterC13C2×#1312
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C2×C4×C8

350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1093241);