Finite Group Databasebeta

C2×#14526879 #16949216

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

Aliases

direct productC2×#14526879

Splittings

SylowC17 ⋊ C2×#1382

Subgroups

subgroupG/H
centerC22×C4#63228
commutatorC8×C17C2×C42
FrattiniC22×C8C22×D17
FittingC2×C17×#427C2
socleC23×C17#102
prime radicalC24×C17SD16
cosocleC22×C8×C17C23
hypercenterC2×#427D17
hypocenterC17C2×#1382
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8 ◁ C2×#427

590 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 84460);