Finite Group Databasebeta

C2×#13112752 #15771893

order3328
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×#13112752

Splittings

SylowC13 ⋊ C2×#1311

Subgroups

subgroupG/H
centerC2×C4×C8C2×D13
commutatorC2×C13C2×C82
FrattiniC4×C8C22×D13
FittingC2×C4×C13×C16C2
socle, prime radicalC23×C13C4×C8
cosocleC4×C8×C13C23
hypercenterC2×C4×C16D13
hypocenterC13C2×#1311
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4×C8 ◁ C2×C4×C16

366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 78542);