Finite Group Databasebeta

C23×C4⋊Dic31 #16858872

order3968
isoclinismisoclinic class of Dic62
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC23×C4⋊Dic31

Splittings

SylowC31 ⋊ C23×C4⋊C4

Subgroups

subgroupG/H
centerC25C2×D31
commutatorC2×C31C24×C4
FrattiniC22C24×D31
FittingC24×C4×C31C2
socle, prime radicalC25×C31C22
cosocleC22×C31C25
hypercenterC24×C4D31
hypocenterC31C23×C4⋊C4
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C25 ◁ C24×C4

2488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3968

Conjugacy classes & character table

1040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 17671);