Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C16 · Schur multiplier (H2) = C43 |
| direct product | C42×C71⋊C16 |
| derived, Sylow | C71 ⋊ C42×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42×C8 | D71 |
| commutator, hypocenter | C71 | C42×C16 |
| Frattini | C22×C8 | C22×D71 |
| Fitting | C42×C8×C71 | C2 |
| socle, prime radical | C23×C71 | C22×C8 |
| cosocle | C22×C8×C71 | C23 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C42×C8 | |
558 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18176 |
4736 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 84387);