Finite Group Databasebeta

C8×#88196 #15832344

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

Aliases

direct productC8×#88196

Splittings

FittingC2×C8×Q8×C13 ⋊ C2
SylowC13 ⋊ C8×#137

Subgroups

subgroupG/H
centerC2×C8C2×C22⋊D13
commutatorC4×C13C23×C8
FrattiniC42C23×D13
FittingC2×C8×Q8×C13C2
socleC22×C13C2×C4×D4
prime radicalC2×#6127C2×C4
cosocleC42×C13C24
hypercenterC2×C8×Q8D13
hypocenterC13C8×#137
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ C2×C8×Q8

714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 138993);