Finite Group Databasebeta

C2×#14527022 #16955460

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#14527022

Splittings

FittingC23×C42×C17 ⋊ C2
SylowC17 ⋊ C2×#1437

Subgroups

subgroupG/H
centerC25C22×D17
commutatorC22×C17C22×C42
FrattiniC24C23×D17
FittingC23×C42×C17C2
socleC25×C17C23
prime radicalC25×D17C22
cosocleC24×C17C24
hypercenterC23×C42D17
hypocenterC17C2×#1437
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C25 ◁ C23×C42

5230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

1136 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 90704);