Finite Group Databasebeta

C22×#19127424 #35370189

order21248
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC22×#19127424

Splittings

FittingC22×C22⋊C8×C83 ⋊ C2
SylowC83 ⋊ C22×#323

Subgroups

subgroupG/H
centerC24(C2×D83)⋊C4
commutatorC22×C83C23×C8
FrattiniC22×C4C23×D83
FittingC22×C22⋊C8×C83C2
socleC24×C83C22⋊C4
prime radicalC25×D83C4
cosocleC22×C4×C83C24
hypercenterC22×C22⋊C8D83
hypocenterC83C22×#323
LCSG ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

2878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

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, 135353);