Finite Group Databasebeta

C2×Q8×#6099 #16727307

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×Q8×#6099

Splittings

SylowC13 ⋊ C2×Q8×M16

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C4×Q8×C13C2
socleC23×C13C23×C4
prime radicalC24×C13C22×C4
cosocleC2×C4×C13C25
hypercenterC22×C4×Q8D13
hypocenterC13C2×Q8×M16
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

2154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033956);