Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1778 |
220 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 113 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 — 3 generators on 23 points:
(1,2,3)(4,6,7,5)(9,15)(14,22)(16,17)(18,23);(8,10,11,20,13,21,12,19)(9,14,16,23,15,22,17,18);(2,3)(4,5,7,6)(8,9,12,17,13,15,11,16)(10,18,20,14,21,23,19,22)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=de,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=cg,h^a=h^2,d^b=dg,e^b=eg84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1778, C2×#69873, #10793293, … |
| maximal normal subgroup of | D3×#1778, C2×#69873, #10793293, … |
| maximal quotient of | #10686385, #10686390, #10686395, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2449);