Finite Group Databasebeta

C22×C22⋊#6092 #16806762

order3328
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C27

Aliases

direct productC22×C22⋊#6092

Splittings

SylowC13 ⋊ C22×C22⋊C16

Subgroups

subgroupG/H
centerC23×C4C2×#261
commutatorC2×C13C23×C16
FrattiniC2×C4C23×#261
FittingC24×C4×C13C4
socleC24×C13C2×C8
prime radicalC25×C13C8
cosocleC2×#1055C24
hypercenterC24×C4#261
hypocenterC13C22×C22⋊C16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C24×C4

1470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113411);