Finite Group Databasebeta

C2×#14545205 #17978837

order4352
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14545205

Splittings

SylowC17 ⋊ C22×M64

Subgroups

subgroupG/H
centerC2×C16C2×#595
commutatorC2×C17C23×C16
FrattiniC8C23×#595
FittingC22×C16×C17C4
socleC22×C17C22×C16
prime radicalC23×D17C16
cosocle#63214C24
hypercenterC22×C16#595
hypocenterC17C22×M64
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C16 ◁ C22×C16

502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114081);