Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C82 · Schur multiplier (H2) = C25×C8 |
| direct product | C22×C8×C67⋊C8 |
| derived, Sylow | C67 ⋊ C22×C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4×C8 | D67 |
| commutator, hypocenter | C67 | C22×C82 |
| Frattini | C42 | C23×D67 |
| Fitting | C22×C4×C8×C67 | C2 |
| socle, prime radical | C24×C67 | C42 |
| cosocle | C42×C67 | C24 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C22×C4×C8 | |
1342 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17152 |
4480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 135134);