Finite Group Databasebeta

C2×#14530395 #17186993

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14530395

Splittings

SylowC17 ⋊ C2×#2112

Subgroups

subgroupG/H
centerC22×C8C22×D17
commutatorC22×C17C23×C8
FrattiniC2×C8C23×D17
FittingC24×C8×C17C2
socleC23×C17C22×C8
prime radicalC25×C17C8
cosocleC2×C8×C17C24
hypercenterC24×C8D17
hypocenterC17C2×#2112
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C8 ◁ C24×C8

1406 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

1136 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 322237);