Finite Group Databasebeta

C2×#14527130 #17000266

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14527130

Splittings

FittingC22×C17×C22⋊C8 ⋊ C2
SylowC17 ⋊ C2×#1468

Subgroups

subgroupG/H
centerC23C2×#63227
commutatorC23×C17C23×C4
FrattiniC22×C4C23×D17
FittingC22×C17×C22⋊C8C2
socleC23×C17C2×C22⋊C4
prime radicalC23×C22⋊D17C4
cosocleC22×C4×C17C24
hypercenterC22×C22⋊C8D17
hypocenterC17C2×#1468
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊C8

1490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 135510);