Finite Group Databasebeta

C22×#11762877 #17898159

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11762877

Splittings

FittingC22×C17×C22⋊C8 ⋊ C2
SylowC17 ⋊ C22×#435

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutatorC22×C17C24×C4
FrattiniC2×C4C24×D17
FittingC22×C17×C22⋊C8C2
socleC24×C17C22×C4
prime radicalC23×C22⋊D17C4
cosocleC2×C4×C17C25
hypercenterC22×C22⋊C8D17
hypocenterC17C22×#435
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

3350 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, 1033403);