Finite Group Databasebeta

#3093×D67 #31723614

order17152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct product#3093×D67

Splittings

FittingC67×#3093 ⋊ C2
SylowC67 ⋊ C2×#3093

Subgroups

subgroupG/H
centerC22C22×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3093C2
socleC22×C67C23×D4
prime radical#525×D67C2
hypercenter#3093D67
hypocenterC67C2×#3093
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3093

2346 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, 1037351);