Finite Group Databasebeta

C2×#471×D67 #31723200

order17152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#471×D67

Splittings

FittingC2×#471×C67 ⋊ C2
SylowC67 ⋊ C22×#471

Subgroups

subgroupG/H
centerC22#121×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#471×C67C2
socleC22×C67C2×#121
prime radicalC2×AGL(1,ℤ/8)×D67C2
hypercenterC2×#471D67
hypocenterC67C22×#471
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#471

2758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1036937);