Finite Group Databasebeta

C22×#11763500 #17941319

order4352
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC22×#11763500

Splittings

FittingC22×C4×Q8×C17 ⋊ C2
SylowC17 ⋊ C22×#552

Subgroups

subgroupG/H
centerC24C23×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC22×C4×Q8×C17C2
socleC24×C17C24
prime radicalC23×D68C22
hypercenterC22×C4×Q8D17
hypocenterC17C22×#552
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C4×Q8

7934 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1076563);