Finite Group Databasebeta

C23×#10587677 #17981032

order4352
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C213×C4

Aliases

direct productC23×#10587677
unambiguous semidirect productD17⋊(C22×#117)

Splittings

FittingC24×C4×C17 ⋊ C4
SylowC17 ⋊ C23×#117

Subgroups

subgroupG/H
centerC23×C4C2×#595
commutatorC2×C17C25×C4
FrattiniC2C25×#595
FittingC24×C4×C17C4
socleC24×C17C22×C4
prime radicalC25×D17C22
cosocleC2×D17C26
hypercenterC24×C4#595
hypocenterC17C23×#117
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C24×C4

14334 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, 1116276);