Finite Group DatabasebetaFinite Group Databasebeta| order | 363 |
| isoclinism | isoclinic class of C112⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C112⋊C3 |
| Fitting, socle, derived, Sylow | C112 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112 | C3 |
| LCS | G ▷ C112 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 33 |
A minimal faithful permutation representation — 2 generators on 33 points:
(1,2,4)(3,7,15)(5,11,19)(6,13,25)(8,18,10)(9,20,14)(12,24,33)(16,21,29)(17,22,31)(23,32,26)(27,30,28);(1,3,8,19,29,32,33,20,30,25,31)(2,14,5,17,12,18,6,26,7,28,16)(4,11,24,13,15,21,9,22,10,23,27)Polycyclic presentation:
3,11^2|b^a=b^7c^10,c^a=b^2c^343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(363, 2);