Finite Group Databasebeta

C2×#14538775 #17902187

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14538775

Splittings

FittingC2×C17×#408 ⋊ C2
SylowC17 ⋊ C2×#3099

Subgroups

subgroupG/H
centerC23C22×D68
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#408C2
socleC23×C17C22×D4
prime radicalC2×#11763387C2
hypercenterC2×#408D17
hypocenterC17C2×#3099
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

2234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1037431);