Finite Group Databasebeta

C23×Dic76 #14578358

order2432
isoclinismisoclinic class of #64516
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC23×Dic76

Splittings

SylowC19 ⋊ C23×Q16

Subgroups

subgroupG/H
centerC24D76
commutator, cosocleC4×C19C25
FrattiniC4C24×D19
FittingC23×C8×C19C2
socle, prime radicalC24×C19D4
hypercenterC23×C8D19
hypocenterC19C23×Q16
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

1464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2432

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18089349, #18089351, #18089375, …
maximal normal subgroup of#18089349, #18089351, #18089375, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 19233);