Finite Group Databasebeta

C2×C22⋊Q8×D31 #16858935

order3968
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×C22⋊Q8×D31

Splittings

FittingC2×C31×C22⋊Q8 ⋊ C2
SylowC31 ⋊ C22×C22⋊Q8

Subgroups

subgroupG/H
centerC23C23×D31
commutator, cosocleC22×C31C25
FrattiniC22C24×D31
FittingC2×C31×C22⋊Q8C2
socleC23×C31C24
prime radicalC24×D31C22
hypercenterC2×C22⋊Q8D31
hypocenterC31C22×C22⋊Q8
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

1840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 992

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 17734);