Finite Group Databasebeta

C22×#11762530 #16999892

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22×#11762530

Splittings

SylowC17 ⋊ C22×#322

Subgroups

subgroupG/H
centerC22×C42C2×D17
commutatorC2×C17C22×C4×C8
FrattiniC42C23×D17
FittingC22×C4×C8×C17C2
socle, prime radicalC24×C17C42
cosocleC42×C17C24
hypercenterC22×C4×C8D17
hypocenterC17C22×#322
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C42 ◁ C22×C4×C8

1182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 135136);