Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#482 ⋊ C2 |
| Sylow | C3 ⋊ #3111 |
392 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2)(4,6,7,10)(5,9,8,11)(12,15,16,17)(13,20,21,19)(14,23,24,25)(18,27,22,26);(2,3)(13,19)(15,17)(18,26)(20,21)(22,27)(23,25);(5,8)(9,11)(12,14,16,24)(13,18,21,22)(15,23,17,25)(19,26,20,27);(4,5)(6,9)(7,8)(10,11)(12,13)(14,22)(15,20)(16,21)(17,19)(18,24)(23,26)(25,27)Polycyclic presentation:
2^7,3|b^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^c=dg,f^c=fg,h^c=h^2,h^d=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3111, C2×#81350, #11663398, … |
| maximal normal subgroup of | D3×#3111, C2×#81350, #11663398, … |
| maximal quotient of | #10795256, #10798210, #10798221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13926);