Finite Group Databasebeta

C8×#88173 #15832297

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

Aliases

direct productC8×#88173

Splittings

FittingC8×C13×Q16 ⋊ C2
SylowC13 ⋊ C8×#135

Subgroups

subgroupG/H
centerC2×C8D4×D13
commutatorC4×C13C23×C8
FrattiniC42C23×D13
FittingC8×C13×Q16C2
socleC22×C13C2×C4×D4
prime radicalC2×#88173C4
cosocleC42×C13C24
hypercenterC8×Q16D13
hypocenterC13C8×#135
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×Q16

750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 138946);