Finite Group Databasebeta

#2986×D67 #31720790

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct product#2986×D67

Splittings

FittingC67×#2986 ⋊ C2
SylowC67 ⋊ C2×#2986

Subgroups

subgroupG/H
center, FrattiniC2×C4C24×D67
commutator, socleC22×C67C24×C4
FittingC67×#2986C2
prime radicalC23×D67C22×C4
cosocleC2×C4×C67C25
hypercenter#2986D67
hypocenterC67C2×#2986
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ #2986

1794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1034527);