Finite Group Databasebeta

C22×C22⋊#6090 #16015584

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

Aliases

direct productC22×C22⋊#6090

Splittings

SylowC13 ⋊ C22×C22⋊C16

Subgroups

subgroupG/H
centerC23×C8C2×D13
commutatorC2×C13C23×C16
FrattiniC2×C8C23×D13
FittingC24×C8×C13C2
socleC24×C13C2×C8
prime radicalC25×C13C8
cosocleC2×C8×C13C24
hypercenterC24×C8D13
hypocenterC13C22×C22⋊C16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C8 ◁ C24×C8

1470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322233);