Finite Group Databasebeta

C22×#11763281 #17940902

order4352
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC22×#11763281

Splittings

FittingC22×C4×D4×C17 ⋊ C2
SylowC17 ⋊ C22×#518

Subgroups

subgroupG/H
centerC24C23×D17
commutatorC2×C17C25×C4
FrattiniC22C25×D17
FittingC22×C4×D4×C17C2
socleC24×C17C24
prime radicalC23×D4×D17C2
cosocleC22×C17C26
hypercenterC22×C4×D4D17
hypocenterC17C22×#518
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C4×D4

14590 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1076146);