Finite Group Databasebeta

C23×#64526 #14578354

order2432
isoclinismisoclinic class of #64525
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC23×#64526

Splittings

SylowC19 ⋊ C23×SD16

Subgroups

subgroupG/H
centerC24C22⋊D19
commutator, cosocleC4×C19C25
FrattiniC4C24×D19
Fitting, prime radicalC23×D4×C19C2
socleC24×C19D4
hypercenterC23×D4D19
hypocenterC19C23×SD16
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×D4

1720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18089341, #18089345, #18089368, …
maximal normal subgroup of#18089341, #18089345, #18089368, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 19229);