Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C67 · Schur multiplier (H2) = C4 |
| direct product | C67×#1410 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | #353 |
| commutator | C42 | C2×C4×C67 |
| Frattini, cosocle | C4⋊Q8 | C22×C67 |
| prime radical | #127×C67 | C4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C22×C67 ◁ C2×C4×C67 ◁ C4⋊Q8×C67 ◁ G | |
104 conjugacy classes of subgroups.
1139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 142);