Finite Group Databasebeta

C2×#14537657 #17898476

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

Aliases

direct productC2×#14537657

Splittings

FittingC2×C17×#520 ⋊ C2
SylowC17 ⋊ C2×#2951

Subgroups

subgroupG/H
centerC23C22×C22⋊D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C17×#520C2
socleC23×C17C22×D4
prime radicalC22×#10587636C2
cosocleC2×C4×C17C25
hypercenterC2×#520D17
hypocenterC17C2×#2951
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

2806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033720);