Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#474 ⋊ C2 |
| Sylow | C3 ⋊ #3076 |
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 27 points:
(2,3)(12,15,17,16)(13,19,20,24)(14,22,23,25)(18,26,27,21);(1,2,3)(12,14)(13,18)(15,22)(16,25)(17,23)(19,26)(20,27)(21,24);(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,f^c=fg,h^d=h^257 conjugacy classes — view the full character table.
| maximal subgroup of | #10771153, #10771157, #10771183, … |
| maximal normal subgroup of | #10771153, #10771157, #10771183, … |
| maximal quotient of | #10794654, #10796128, #10797343, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13540);