Finite Group Databasebeta

C2×#13113123 #15828516

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13113123

Splittings

SylowC13 ⋊ C2×#1451

Subgroups

subgroupG/H
centerC2×C42C22×D13
commutatorC22×C13C22×C42
FrattiniC42C23×D13
FittingC2×C4×C13×M16C2
socleC23×C13C2×C42
prime radicalC24×C13C42
cosocleC42×C13C24
hypercenterC2×C4×M16D13
hypocenterC13C2×#1451
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C2×C4×M16

966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 135165);