Finite Group Databasebeta

C2×C8×#6131 #16727352

order3328
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC2×C8×#6131

Splittings

FittingC2×C8×Q8×C13 ⋊ C2
SylowC13 ⋊ C2×C8×#41

Subgroups

subgroupG/H
centerC22×C8C22×D13
commutatorC2×C13C24×C8
FrattiniC2×C4C24×D13
FittingC2×C8×Q8×C13C2
socleC23×C13C23×C4
prime radicalC22×#6131C4
cosocleC2×C4×C13C25
hypercenterC2×C8×Q8D13
hypocenterC13C2×C8×#41
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C2×C8×Q8

2566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1034001);