Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3078 |
376 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 143 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:
(1,2,3)(13,18)(17,26)(19,23)(20,27);(12,14,16,22)(13,17,18,26)(15,24,25,21)(19,27,23,20);(2,3)(4,6,7,11)(5,8,9,10);(4,5,7,9)(6,10,11,8)(12,13)(14,20)(15,23)(16,18)(17,21)(19,25)(22,27)(24,26)Polycyclic presentation:
2^7,3|a^2=e,b^2=e,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^b=h^2,f^c=fg54 conjugacy classes — view the full character table.
| maximal subgroup of | #10829435, #10829439, #10829446, … |
| maximal normal subgroup of | #10829435, #10829439, #10829446, … |
| maximal quotient of | #10794672, #10796150, #10796155, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11525);