Finite Group Databasebeta

C2×#13115116 #15863999

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13115116

Splittings

SylowC13 ⋊ C2×#1867

Subgroups

subgroupG/H
centerC23#88191
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC2×C13×#386C2
socleC23×C13#120
prime radicalC23×D4×C13C22
cosocleC24×C13C24
hypercenterC2×#386D13
hypocenterC13C2×#1867
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C2×#386

1994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 170648);