Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3076 |
388 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)(12,15,17,16)(13,19,20,24)(14,22,23,25)(18,26,27,21);(12,14)(13,18)(15,22)(16,25)(17,23)(19,26)(20,27)(21,24);(2,3)(4,6,7,11)(5,8,9,10);(4,5,7,9)(6,10,11,8)(12,13)(14,21)(15,19)(16,24)(17,20)(18,22)(23,26)(25,27)Polycyclic presentation:
2^7,3|a^2=e,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^2,f^c=fg66 conjugacy classes — view the full character table.
| maximal subgroup of | #10803013, #10803014, #10803024, … |
| maximal normal subgroup of | #10803013, #10803014, #10803024, … |
| maximal quotient of | #10794657, #10796131, #10796137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11398);