Finite Group Databasebeta

C22×C22⋊#63216 #17978167

order4352
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C27

Aliases

direct productC22×C22⋊#63216

Splittings

SylowC17 ⋊ C22×C22⋊C16

Subgroups

subgroupG/H
centerC23×C4C2×#595
commutatorC2×C17C23×C16
FrattiniC2×C4C23×#595
FittingC24×C4×C17C4
socleC24×C17C2×C8
prime radicalC25×C17C8
cosocleC2×#3622C24
hypercenterC24×C4#595
hypocenterC17C22×C22⋊C16
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C24×C4

1470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1113411);