Finite Group Databasebeta

C2×#22561386 #30883269

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22561386

Splittings

SylowC67 ⋊ C2×#2032

Subgroups

subgroupG/H
centerC22#16863308
commutator, cosocleC24×C67C24
FrattiniC24C23×D67
FittingC22×#99×C67C2
socleC22×C67#393
prime radicalC23×D4×C67C22
hypercenterC22×#99D67
hypocenterC67C2×#2032
LCSG ▷ C24×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

1434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1498 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 197006);