Finite Group Databasebeta

C22×#11762669 #17192584

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC22×#11762669

Splittings

SylowC17 ⋊ C22×#380

Subgroups

subgroupG/H
centerC25C22×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC25×C4×C17C2
socleC25×C17C23
prime radicalC26×C17C22
cosocleC23×C17C25
hypercenterC25×C4D17
hypocenterC17C22×#380
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C25 ◁ C25×C4

8670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

1136 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 327828);