Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1517 |
264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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) = 96 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,3)(4,6,8,7)(5,9,11,10)(12,15,16,24)(13,18,19,27)(14,21,22,23)(17,25,20,26);(5,9)(6,7)(10,11)(12,14)(13,17)(15,23)(16,22)(18,26)(19,20)(21,24)(25,27);(2,3)(4,5)(6,10)(7,9)(8,11)(12,13)(14,20,22,17)(15,18)(16,19)(21,26,23,25)(24,27)Polycyclic presentation:
2^7,3|a^2=e,c^2=f,d^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^2,c^b=cf,d^b=dg,e^b=efg60 conjugacy classes — view the full character table.
| maximal subgroup of | #10687150, #10687153, #10687156, … |
| maximal normal subgroup of | #10687150, #10687153, #10687156, … |
| maximal quotient of | #10683181, #10683243, #10683247, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4390);