Finite Group Databasebeta

C2×#13115773 #15867361

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#13115773

Splittings

SylowC13 ⋊ C2×#1984

Subgroups

subgroupG/H
centerC23×C4C22×D13
commutatorC22×C13C23×C8
FrattiniC22×C4C23×D13
FittingC22×C4×Q8×C13C2
socle, prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenterC22×C4×Q8D13
hypocenterC13C2×#1984
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C4×Q8

1502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 174010);