Finite Group Databasebeta

C2×#14529138 #17035663

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#14529138

Splittings

FittingC2×C17×#336 ⋊ C2
SylowC17 ⋊ C2×#1880

Subgroups

subgroupG/H
centerC24C2×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#336C2
socleC24×C17C2×D4
prime radicalC23×D68C22
cosocleC22×C4×C17C24
hypercenterC2×#336D17
hypocenterC17C2×#1880
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

2038 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 170907);