Finite Group Databasebeta

C23×Dic1076 #46825608

order34432
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC23×Dic1076

Splittings

SylowC269 ⋊ C23×Q16

Subgroups

subgroupG/H
centerC24D1076
commutator, cosocleC4×C269C25
FrattiniC4C24×D269
FittingC23×C8×C269C2
socle, prime radicalC24×C269D4
hypercenterC23×C8D269
hypocenterC269C23×Q16
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

1464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34432

Conjugacy classes & character table

8632 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 19233);