Finite Group Databasebeta

C22×#16863287 #31014158

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×#16863287

Splittings

FittingC23×C42×C67 ⋊ C2
SylowC67 ⋊ C22×#388

Subgroups

subgroupG/H
centerC25C22×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC23×C42×C67C2
socleC25×C67C23
prime radicalC25×D67C22
cosocleC23×C67C25
hypercenterC23×C42D67
hypocenterC67C22×#388
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C25 ◁ C23×C42

5966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

4336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 327895);