Finite Group Databasebeta

C2×#14543746 #17958743

order4352
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#14543746

Splittings

SylowC17 ⋊ C2×#1335

Subgroups

subgroupG/H
centerC2×C4#10587547
commutatorC8×C17C22×C8
FrattiniC2×C8C22×#595
Fitting, prime radicalC2×C17×#135C4
socleC22×C17D4⋊C8
cosocleC8×Dic17C23
hypercenterC2×#135#595
hypocenterC17C2×#1335
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#135

414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1093987);