Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#419 ⋊ C2 |
| Sylow | C3 ⋊ #2949 |
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(8,10)(9,14)(11,17)(12,16)(13,20)(15,22)(18,23)(19,21);(2,3)(4,6,7,5)(10,16)(14,22)(17,23)(20,21);(8,9,12,15)(10,14,16,22)(11,19,18,13)(17,21,23,20);(4,5,7,6)(9,13)(10,16)(11,18)(14,21)(15,19)(20,22)Polycyclic presentation:
2^7,3|a^2=f,b^2=g,c^2=f,e^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,d^c=dg,h^c=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | #10809085, #10809087, #10811094, … |
| maximal normal subgroup of | #10809085, #10809087, #10811094, … |
| maximal quotient of | #10764648, #10764863, #10764879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11523);