Finite Group Databasebeta

C22×#99×D17 #17897783

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

Aliases

direct productC22×#99×D17

Splittings

FittingC22×C17×#99 ⋊ C2
SylowC17 ⋊ C23×#99

Subgroups

subgroupG/H
centerC23C22⋊C4×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC22×C17×#99C2
socleC23×C17C2×C22⋊C4
prime radicalC23×D4×D17C2
cosocleC23×C17C25
hypercenterC22×#99D17
hypocenterC17C23×#99
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25 ◁ C22×#99

7902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033027);