Finite Group Databasebeta

C2×#14526627 #16923912

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14526627

Splittings

SylowC17 ⋊ C2×#1280

Subgroups

subgroupG/H
centerC24C22⋊Dic17
commutatorC22×C17C2×C4×C8
FrattiniC23×C4C22×D17
FittingC22×C17×#95C2
socleC24×C17C22⋊C4
prime radicalC25×C17C2×C4
cosocleC23×C4×C17C23
hypercenterC22×#95D17
hypocenterC17C2×#1280
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×#95

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 59156);