Finite Group Databasebeta

C2×#14537660 #17898479

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14537660

Splittings

SylowC17 ⋊ C2×#2951

Subgroups

subgroupG/H
centerC23C2×D4×D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
Fitting, prime radicalC22×C17×#135C2
socleC23×C17C22×D4
cosocleC2×C4×C17C25
hypercenterC22×#135D17
hypocenterC17C2×#2951
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#135

2806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033723);