Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3108 |
390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2,3)(4,6,7,10)(5,9,8,11);(2,3)(12,14,15,21)(13,18,17,26)(16,25,23,22)(19,27,24,20);(5,8)(9,11)(13,17)(18,26)(19,24)(20,27);(4,5)(6,9)(7,8)(10,11)(12,13)(14,20)(15,17)(16,24)(18,22)(19,23)(21,27)(25,26)Polycyclic presentation:
2^7,3|c^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,f^c=fg,h^c=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | #10690392, #10690394, #10765166, … |
| maximal normal subgroup of | #10690392, #10690394, #10765166, … |
| maximal quotient of | #10795202, #10798142, #10798186, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15728);