Finite Group Databasebeta

C23×#64528 #14578357

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

Aliases

direct productC23×#64528

Splittings

SylowC19 ⋊ C23×Q16

Subgroups

subgroupG/H
centerC24C22⋊D19
commutator, cosocleC4×C19C25
FrattiniC4C24×D19
FittingC23×Q8×C19C2
socle, prime radicalC24×C19D4
hypercenterC23×Q8D19
hypocenterC19C23×Q16
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×Q8

1464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2432

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18089347, #18089348, #18089374, …
maximal normal subgroup of#18089347, #18089348, #18089374, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 19232);