Finite Group Databasebeta

C2×#14526636 #16924035

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#14526636

Splittings

SylowC17 ⋊ C2×#1284

Subgroups

subgroupG/H
centerC23#10587502
commutatorC2×C4×C17C2×C42
FrattiniC23×C4C22×D17
FittingC2×C17×#381C2
socleC23×C17#95
prime radicalC25×C17D4
cosocleC23×C4×C17C23
hypercenterC2×#381D17
hypocenterC17C2×#1284
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#381

1118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 59279);