Finite Group Databasebeta

C23×#10587477 #17897784

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC23×#10587477

Splittings

FittingC23×C22⋊C4×C17 ⋊ C2
SylowC17 ⋊ C23×#99

Subgroups

subgroupG/H
centerC24#63227
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC23×C22⋊C4×C17C2
socleC24×C17C22⋊C4
prime radicalC24×C22⋊D17C2
cosocleC23×C17C25
hypercenterC23×C22⋊C4D17
hypocenterC17C23×#99
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C26 ◁ C23×C22⋊C4

7902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033028);