Finite Group Databasebeta

C23×#92469 #16860412

order3968
isoclinismisoclinic class of Dic62
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC23×#92469

Splittings

FittingC23×C8×C31 ⋊ C2
SylowC31 ⋊ C23×M16

Subgroups

subgroupG/H
centerC23×C4C2×D31
commutatorC2×C31C24×C4
FrattiniC4C24×D31
FittingC23×C8×C31C2
socleC24×C31C2×C4
prime radicalC24×D31C4
cosocleC4×C31C25
hypercenterC23×C8D31
hypocenterC31C23×M16
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C23×C4 ◁ C23×C8

1720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

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, 19211);