Finite Group Databasebeta

C22×#19127635 #35570619

order21248
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#19127635

Splittings

SylowC83 ⋊ C22×#398

Subgroups

subgroupG/H
centerC25C22×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC22×#95×C83C2
socle, prime radicalC25×C83C23
hypercenterC22×#95D83
hypocenterC83C22×#398
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C25 ◁ C22×#95

4158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21248

Conjugacy classes & character table

3368 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 335783);