Finite Group Databasebeta

C22×C22⋊(C83⋊C16) #35557069

order21248
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C27

Aliases

direct productC22×C22⋊(C83⋊C16)

Splittings

SylowC83 ⋊ C22×C22⋊C16

Subgroups

subgroupG/H
centerC23×C8C2×D83
commutatorC2×C83C23×C16
FrattiniC2×C8C23×D83
FittingC24×C8×C83C2
socleC24×C83C2×C8
prime radicalC25×C83C8
cosocleC2×C8×C83C24
hypercenterC24×C8D83
hypocenterC83C22×C22⋊C16
LCSG ▷ C2×C83 ▷ C83
UCSC1 ◁ C23×C8 ◁ C24×C8

1470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

5408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 322233);