Finite Group Databasebeta

#2047×D67 #30883625

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

Aliases

direct product#2047×D67

Splittings

FittingC67×#2047 ⋊ C2
SylowC67 ⋊ C2×#2047

Subgroups

subgroupG/H
centerC22#121×D67
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
FittingC67×#2047C2
socleC22×C67C2×#121
prime radicalC23×D67#41
hypercenter#2047D67
hypocenterC67C2×#2047
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2047

1330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 197362);