Finite Group Databasebeta

C23×#92482 #16860433

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

Aliases

direct productC23×#92482

Splittings

SylowC31 ⋊ C23×Q16

Subgroups

subgroupG/H
centerC24C22⋊D31
commutator, cosocleC4×C31C25
FrattiniC4C24×D31
FittingC23×Q8×C31C2
socle, prime radicalC24×C31D4
hypercenterC23×Q8D31
hypocenterC31C23×Q16
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×Q8

1464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3968

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, 19232);