Finite Group Databasebeta

C22×#11762676 #17192601

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#11762676

Splittings

SylowC17 ⋊ C22×#383

Subgroups

subgroupG/H
centerC25C22×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC22×C17×#95C2
socle, prime radicalC25×C17C23
cosocleC23×C17C25
hypercenterC22×#95D17
hypocenterC17C22×#383
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C25 ◁ C22×#95

3678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 327845);