Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#357 ⋊ C2 |
| Sylow | C3 ⋊ C4×D16 |
174 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 59 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:
(2,3)(4,6,7,5);(1,2,3)(9,13)(10,17)(11,18)(14,15)(16,22)(19,23)(20,21);(4,5,7,6)(8,9)(10,13)(11,20)(12,16)(14,17)(15,18)(19,22)(21,23)Polycyclic presentation:
2^7,3|a^2=e,c^2=e,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,d^b=df,f^b=fg,h^c=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×D16, C2×#69174, #10948465, … |
| maximal normal subgroup of | C4×D3×D16, C2×#69174, #10948465, … |
| maximal quotient of | #10706906, #10707079, #10707085, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1750);