Finite Group Databasebeta

C8×#88207 #15868414

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC8×#88207

Splittings

FittingC24×C8×C13 ⋊ C2
SylowC13 ⋊ C8×#120

Subgroups

subgroupG/H
centerC22×C8C22×D13
commutatorC22×C13C23×C8
FrattiniC22×C4C23×D13
FittingC24×C8×C13C2
socleC23×C13C23×C4
prime radicalC2×#88207C4
cosocleC22×C4×C13C24
hypercenterC24×C8D13
hypocenterC13C8×#120
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C24×C8

1786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 175063);