Finite Group Databasebeta

C23×Dic718 #37527267

order22976
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC23×Dic718

Splittings

SylowC359 ⋊ C23×Q8

Subgroups

subgroupG/H
centerC24C2×D359
commutator, cosocleC2×C359C25
FrattiniC2C24×D359
FittingC23×C4×C359C2
socle, prime radicalC24×C359C22
hypercenterC23×C4D359
hypocenterC359C23×Q8
LCSG ▷ C2×C359 ▷ C359
UCSC1 ◁ C24 ◁ C23×C4

850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22976

Conjugacy classes & character table

5768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 1373);