Finite Group Databasebeta

C23×Q8×D31 #16860505

order3968
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC23×Q8×D31

Splittings

FittingC23×Q8×C31 ⋊ C2
SylowC31 ⋊ C24×Q8

Subgroups

subgroupG/H
centerC24C22×D31
commutator, cosocleC2×C31C26
FrattiniC2C25×D31
FittingC23×Q8×C31C2
socleC24×C31C23
prime radicalC24×D31C22
hypercenterC23×Q8D31
hypocenterC31C24×Q8
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C24 ◁ C23×Q8

6264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 19304);