Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#465 ⋊ C2 |
| Sylow | C3 ⋊ #3057 |
492 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 23 points:
(2,3)(10,16)(14,21)(17,22)(19,23);(1,2,3)(5,7)(8,10)(9,14)(11,17)(12,16)(13,19)(15,21)(18,22)(20,23);(8,9,11,13,12,15,18,20)(10,14,17,19,16,21,22,23);(4,5)(6,7)(9,13)(11,18)(14,19)(15,20)(17,22)(21,23)Polycyclic presentation:
2^7,3|b^2=e,e^2=g,b^a=be,c^a=cf,e^a=eg,d^c=dg,h^d=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3057, C2×#80659, #11662403, … |
| maximal normal subgroup of | D3×#3057, C2×#80659, #11662403, … |
| maximal quotient of | #10778244, #10778283, #10778322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13235);