Finite Group Databasebeta

C23×#92480 #16860430

order3968
isoclinismisoclinic class of #92479
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC23×#92480

Splittings

SylowC31 ⋊ C23×SD16

Subgroups

subgroupG/H
centerC24C22⋊D31
commutator, cosocleC4×C31C25
FrattiniC4C24×D31
Fitting, prime radicalC23×D4×C31C2
socleC24×C31D4
hypercenterC23×D4D31
hypocenterC31C23×SD16
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×D4

1720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 19229);