Finite Group Databasebeta

C23×#64520 #14578337

order2432
isoclinismisoclinic class of Dic38
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC23×#64520

Splittings

SylowC19 ⋊ C23×M16

Subgroups

subgroupG/H
centerC23×C4C2×D19
commutatorC2×C19C24×C4
FrattiniC4C24×D19
FittingC24×C4×C19C2
socleC24×C19C2×C4
prime radicalC25×C19C4
cosocleC4×C19C25
hypercenterC24×C4D19
hypocenterC19C23×M16
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C23×C4 ◁ C24×C4

1720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18087766, #18087768, #18087774, …
maximal normal subgroup of#18087766, #18087768, #18087774, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 19212);