Finite Group Databasebeta

C2×#14541935 #17940848

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14541935

Splittings

FittingC2×C17×#578 ⋊ C2
SylowC17 ⋊ C2×#3417

Subgroups

subgroupG/H
centerC22C22×#63228
commutator, cosocleC8×C17C25
FrattiniC8C24×D17
FittingC2×C17×#578C2
socleC22×C17C22×D8
hypercenterC2×#578D17
hypocenterC17C2×#3417
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ C2×#578

2022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1076092);