Finite Group DatabasebetaFinite Group Databasebeta| order | 333 |
| isoclinism | isoclinic class of C37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C37 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C37⋊C3 |
| commutator, hypocenter | C37 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C37 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C3 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 333 |
A minimal faithful permutation representation — 2 generators on 46 points:
(2,3,5)(4,7,12)(6,10,9)(8,14,21)(11,16,18)(13,19,15)(17,24,28)(20,26,25)(22,29,23)(27,32,33)(30,34,31)(35,37,36)(38,39,41,40,42,44,43,45,46);(1,2,4,8,14,22,30,35,34,19,5,9,15,23,24,7,13,20,27,29,12,18,25,31,32,16,3,6,11,17,21,28,33,36,37,26,10)Polycyclic presentation:
3^2,37|a^3=b,c^a=c^2645 conjugacy classes — view the full character table.
| maximal subgroup of | #66524⋊C2, C2×#66524, #11758603, … |
| maximal normal subgroup of | #66524⋊C2, C2×#66524, #11758603, … |
| maximal quotient of | C2×#66524, #11758601, C3×#66524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(333, 1);