Finite Group Databasebeta

C22×#11763251 #17940823

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11763251

Splittings

FittingC22×C17×Q32 ⋊ C2
SylowC17 ⋊ C22×#510

Subgroups

subgroupG/H
centerC23D8×D17
commutator, cosocleC8×C17C25
FrattiniC8C24×D17
FittingC22×C17×Q32C2
socleC23×C17C2×D8
prime radicalC22×#10587605C2
hypercenterC22×Q32D17
hypocenterC17C22×#510
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q32

2078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1076067);