Finite Group Databasebeta

C22×#11763249 #17940821

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

Aliases

direct productC22×#11763249

Splittings

SylowC17 ⋊ C22×#510

Subgroups

subgroupG/H
centerC23C2×#63228
commutator, cosocleC8×C17C25
FrattiniC8C24×D17
Fitting, prime radicalC22×C17×#135C2
socleC23×C17C2×D8
hypercenterC22×#135D17
hypocenterC17C22×#510
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×#135

2078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1076065);