Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#441 ⋊ C2 |
| Sylow | C3 ⋊ #2943 |
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 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) = 192 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2)(8,11,13,12)(9,16,15,20)(10,18,19,21)(14,23,22,17);(4,6,7,5)(9,15)(14,22)(16,20)(17,23);(2,3)(8,10)(9,14)(11,18)(12,21)(13,19)(15,22)(16,23)(17,20);(4,5,7,6)(8,9)(10,17)(11,16)(12,20)(13,15)(14,18)(19,23)(21,22)Polycyclic presentation:
2^7,3|a^2=f,c^2=f,d^2=g,e^2=g,b^a=be,c^a=cg,e^a=eg,e^b=eg,h^b=h^2,h^d=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | #10948632, D3×#2943, C2×#79828, … |
| maximal normal subgroup of | #10948632, D3×#2943, C2×#79828, … |
| maximal quotient of | #10764592, #10764758, #10764963, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12404);