Finite Group Databasebeta

C22×#11763113 #17901810

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC22×#11763113

Splittings

SylowC17 ⋊ C22×#479

Subgroups

subgroupG/H
centerC24C2×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC22×C17×#125C2
socle, prime radicalC24×C17C2×D4
hypercenterC22×#125D17
hypocenterC17C22×#479
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#125

2142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1037054);