Finite Group Databasebeta

C23×Dic922 #44442900

order29504
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC23×Dic922

Splittings

SylowC461 ⋊ C23×Q8

Subgroups

subgroupG/H
centerC24C2×D461
commutator, cosocleC2×C461C25
FrattiniC2C24×D461
FittingC23×C4×C461C2
socle, prime radicalC24×C461C22
hypercenterC23×C4D461
hypocenterC461C23×Q8
LCSG ▷ C2×C461 ▷ C461
UCSC1 ◁ C24 ◁ C23×C4

850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29504

Conjugacy classes & character table

7400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 1373);