Finite Group Databasebeta

C2×#14545386 #17979477

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#14545386

Splittings

FittingC22×#41×C17 ⋊ C4
SylowC17 ⋊ C2×#2884

Subgroups

subgroupG/H
centerC22C22×C22⋊#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC22×#41×C17C4
socleC22×C17C22×C22⋊C4
prime radicalC22×#10587697C2
cosocleC22×D17C25
hypercenterC22×#41#595
hypocenterC17C2×#2884
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×Q8 ◁ C22×#41

4818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

242 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114721);