Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
| direct product | #2509×D71 |
| Fitting | C71×#2509 ⋊ C2 |
| Sylow | C71 ⋊ C2×#2509 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D71 |
| commutator, socle, cosocle | C23×C71 | C25 |
| Fitting | C71×#2509 | C2 |
| prime radical | C23×D71 | C24 |
| hypercenter | #2509 | D71 |
| hypocenter | C71 | C2×#2509 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #2509 | |
1966 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9088 |
1406 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 339030);