Finite Group Databasebeta

C22×#11762591 #17187010

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#11762591

Splittings

SylowC17 ⋊ C22×#349

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic17
commutatorC22×C17C23×C8
FrattiniC2×C8C23×D17
FittingC23×M16×C17C2
socleC23×C17C22⋊C8
prime radicalC25×C17C8
cosocleC2×C8×C17C24
hypercenterC23×M16D17
hypocenterC17C22×#349
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C23×M16

1262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 322254);