Finite Group Databasebeta

C2×#14528827 #17033963

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

Aliases

direct productC2×#14528827

Splittings

FittingC2×C17×#427 ⋊ C2
SylowC17 ⋊ C2×#1812

Subgroups

subgroupG/H
centerC2×C4#10587578
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#427C2
socleC22×C17#380
prime radicalC22×#63252C22
cosocleC22×C4×C17C24
hypercenterC2×#427D17
hypocenterC17C2×#1812
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#427

1346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 169207);