Finite Group Databasebeta

C2×#14526893 #16949247

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14526893

Splittings

SylowC17 ⋊ C2×#1387

Subgroups

subgroupG/H
centerC23#10587492
commutatorC8×C17C2×C42
FrattiniC22×C8C22×D17
FittingC22×C17×M32C2
socleC23×C17#102
prime radicalC24×C17SD16
cosocleC22×C8×C17C23
hypercenterC22×M32D17
hypocenterC17C2×#1387
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 84491);