Finite Group Databasebeta

Q8×#88155 #16727330

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

Aliases

direct productQ8×#88155

Splittings

FittingC2×C8×Q8×C13 ⋊ C2
SylowC13 ⋊ Q8×#131

Subgroups

subgroupG/H
centerC2×C8C23×D13
commutator, socleC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC2×C8×Q8×C13C2
prime radicalC2×#6127C23
cosocleC2×C4×C13C25
hypercenterC2×C8×Q8D13
hypocenterC13Q8×#131
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C2×C8×Q8

1882 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, 1033979);