Finite Group Databasebeta

C2×#13112914 #15777756

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13112914

Splittings

SylowC13 ⋊ C2×#1374

Subgroups

subgroupG/H
centerC23×C8C2×D13
commutatorC2×C13C2×C4×C16
FrattiniC22×C8C22×D13
FittingC22×C4×C8×C13C2
socle, prime radicalC24×C13C2×C8
cosocleC22×C8×C13C23
hypercenterC22×C4×C8D13
hypocenterC13C2×#1374
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C8 ◁ C22×C4×C8

726 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, 84405);