Finite Group Databasebeta

C2×#14528623 #17032156

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#14528623

Splittings

FittingC2×C17×#405 ⋊ C2
SylowC17 ⋊ C2×#1764

Subgroups

subgroupG/H
centerC22×C8C22⋊D17
commutatorC4×C17C22×C42
FrattiniC22×C4C23×D17
FittingC2×C17×#405C2
socleC23×C17C4×D4
prime radicalC22×#63252C22
cosocleC22×C4×C17C24
hypercenterC2×#405D17
hypocenterC17C2×#1764
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C2×#405

1558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 167400);