Finite Group Databasebeta

C22⋊Q8×Dic31 #16848247

order3968
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22⋊Q8×Dic31

Splittings

SylowC31 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC2×C31×C22⋊Q8C2
socle, cosocleC23×C31C24
prime radicalC24×C31C23
hypercenterC2×C22⋊Q8D31
hypocenterC31C4×C22⋊Q8
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

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, 7046);