Finite Group Databasebeta

C22×#11762937 #17898679

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC22×#11762937

Splittings

SylowC17 ⋊ C22×#446

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutatorC22×C17C24×C4
FrattiniC2×C4C24×D17
FittingC22×C17×#97C2
socle, prime radicalC24×C17C22×C4
cosocleC2×C4×C17C25
hypercenterC22×#97D17
hypocenterC17C22×#446
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C22×#97

2222 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, 1033923);