Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C71 · Schur multiplier (H2) = C28 |
| direct product | C71×#7557 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25×C71 | C23 |
| commutator | C23 | C2×C42×C71 |
| Frattini, cosocle | C25 | C23×C71 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25×C71 ◁ G | |
2886 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18176 |
6248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 545);