Finite Group Databasebeta

C22×#123×D17 #17940969

order4352
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC22×#123×D17

Splittings

FittingC22×C17×#123 ⋊ C2
SylowC17 ⋊ C23×#123

Subgroups

subgroupG/H
centerC24C23×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC22×C17×#123C2
socleC24×C17C24
prime radicalC23×D4×D17C2
hypercenterC22×#123D17
hypocenterC17C23×#123
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×#123

15150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1076213);