Finite Group Databasebeta

C2×#22559237 #30827976

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#22559237

Splittings

SylowC67 ⋊ C2×#1615

Subgroups

subgroupG/H
centerC23#14524011
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
FittingC2×#481×C67C2
socleC23×C67#120
prime radicalC2×#121×C67C22
hypercenterC2×#481D67
hypocenterC67C2×#1615
LCSG ▷ C22×C4×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

1016 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 141713);