Finite Group Databasebeta

C2×#14537685 #17898627

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

Aliases

direct productC2×#14537685

Splittings

FittingC22×C17×#131 ⋊ C2
SylowC17 ⋊ C2×#2955

Subgroups

subgroupG/H
centerC2×C8C2×C22⋊D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC22×C17×#131C2
socleC22×C17C2×C4×D4
prime radicalC2×#11763607C2
cosocleC2×C4×C17C25
hypercenterC22×#131D17
hypocenterC17C2×#2955
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C23×C8 ◁ C22×#131

2666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033871);