Finite Group Databasebeta

C23×#10587569 #17940971

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

Aliases

direct productC23×#10587569

Splittings

FittingC23×C22⋊C4×C17 ⋊ C2
SylowC17 ⋊ C23×#123

Subgroups

subgroupG/H
centerC25C22×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC23×C22⋊C4×C17C2
socleC25×C17C23
prime radicalC24×C22⋊D17C2
hypercenterC23×C22⋊C4D17
hypocenterC17C23×#123
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C25 ◁ C23×C22⋊C4

15150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 1076215);