Finite Group Databasebeta

C2×#14528101 #17015457

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14528101

Splittings

SylowC17 ⋊ C2×#1661

Subgroups

subgroupG/H
centerC23#10587639
commutator, cosocleC42×C17C24
FrattiniC42C23×D17
Fitting, prime radicalC2×C17×#562C2
socleC23×C17#120
hypercenterC2×#562D17
hypocenterC17C2×#1661
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#562

1022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 150701);