Finite Group Databasebeta

C2×#14527096 #17000116

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#14527096

Splittings

FittingC2×C17×#431 ⋊ C2
SylowC17 ⋊ C2×#1458

Subgroups

subgroupG/H
centerC22×C4#63227
commutatorC22×C17C23×C8
FrattiniC22×C4C23×D17
FittingC2×C17×#431C2
socleC23×C17C2×C22⋊C4
prime radicalC24×D17C2×C4
cosocleC22×C4×C17C24
hypercenterC2×#431D17
hypocenterC17C2×#1458
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#431

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 135360);