Finite Group Databasebeta

C23×#64515 #14578336

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

Aliases

direct productC23×#64515

Splittings

FittingC23×C8×C19 ⋊ C2
SylowC19 ⋊ C23×M16

Subgroups

subgroupG/H
centerC23×C4C2×D19
commutatorC2×C19C24×C4
FrattiniC4C24×D19
FittingC23×C8×C19C2
socleC24×C19C2×C4
prime radicalC24×D19C4
cosocleC4×C19C25
hypercenterC23×C8D19
hypocenterC19C23×M16
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C23×C4 ◁ C23×C8

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#18087765, #18087790, #18087796
maximal normal subgroup of#18087765, #18087790, #18087796

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 19211);