Finite Group Databasebeta

C8×#88200 #15870327

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

Aliases

direct productC8×#88200

Splittings

FittingC2×C8×Q8×C13 ⋊ C2
SylowC13 ⋊ C8×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C8C22×D13
commutatorC22×C13C23×C8
FrattiniC22×C4C23×D13
FittingC2×C8×Q8×C13C2
socleC23×C13C23×C4
prime radicalC23×D13C22×C4
cosocleC22×C4×C13C24
hypercenterC2×C8×Q8D13
hypocenterC13C8×C22⋊Q8
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C2×C8×Q8

990 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, 176976);