Finite Group Databasebeta

C22×#11763777 #17979436

order4352
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C211

Aliases

direct productC22×#11763777

Splittings

SylowC17 ⋊ C23×C22⋊C8

Subgroups

subgroupG/H
centerC23×C4C2×#595
commutatorC2×C17C24×C8
FrattiniC22C24×#595
FittingC24×C4×C17C4
socleC24×C17C22×C4
prime radicalC25×D17C4
cosocleC2×Dic17C25
hypercenterC24×C4#595
hypocenterC17C23×C22⋊C8
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C24×C4

7646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 1114680);