Finite Group Databasebeta

C22×#19127613 #35570584

order21248
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productC22×#19127613

Splittings

SylowC83 ⋊ C22×#393

Subgroups

subgroupG/H
centerC25C22×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC23×C22⋊C4×C83C2
socleC25×C83C23
prime radicalC26×C83C22
hypercenterC23×C22⋊C4D83
hypocenterC83C22×#393
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C25 ◁ C23×C22⋊C4

7118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

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, 335748);