Finite Group DatabasebetaFinite Group Databasebeta| order | 999 |
| isoclinism | isoclinic class of #66526 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C37 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #66526 |
| commutator, hypocenter | C37 | C27 |
| Fitting, socle, prime radical | C3×C37 | C9 |
| cosocle | #66524 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 64 |
| transitive degree | μt(G) = 999 |
Polycyclic presentation:
3^3,37|a^3=b,b^3=c,d^a=d^16,d^b=d^2639 conjugacy classes — view the full character table.
| maximal subgroup of | #11758603⋊C2, C2×#11758603, C3×#11758603, … |
| maximal normal subgroup of | #11758603⋊C2, C2×#11758603, C3×#11758603, … |
| maximal quotient of | C2×#11758603, #15688534, C3×#11758603 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(999, 3);