Finite Group Databasebeta

C2×#14545940 #17983003

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14545940

Splittings

SylowC17 ⋊ C22×#346

Subgroups

subgroupG/H
centerC22×C4C2×#3633
commutatorC2×C17C22×C4×C8
FrattiniC22C23×#3633
FittingC2×C42×C17C8
socleC23×C17C22×C8
prime radicalC23×D17C2×C8
cosocleC2×#3624C24
hypercenterC2×C42#3633
hypocenterC17C22×#346
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42

942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1118247);