Finite Group Databasebeta

C22×Q8×Dic31 #16858887

order3968
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×Q8×Dic31

Splittings

SylowC31 ⋊ C22×C4×Q8

Subgroups

subgroupG/H
centerC24C22×D31
commutatorC2×C31C24×C4
FrattiniC22C24×D31
FittingC23×Q8×C31C2
socle, prime radicalC24×C31C23
cosocleC22×C31C25
hypercenterC23×Q8D31
hypocenterC31C22×C4×Q8
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C24 ◁ C23×Q8

1664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3968

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, 17686);