Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×C4×D8 ⋊ C2 |
| Sylow | C3 ⋊ #2206 |
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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)(9,13)(10,17)(11,18)(14,15)(16,22)(19,23)(20,21);(4,5,6,7);(2,3)(5,7)(8,9)(10,13)(11,20)(12,16)(14,17)(15,18)(19,22)(21,23)Polycyclic presentation:
2^7,3|b^2=d,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,e^c=ef,f^c=fg57 conjugacy classes — view the full character table.
| maximal subgroup of | #10708611, #10708614, #10708632, … |
| maximal normal subgroup of | #10708611, #10708614, #10708632, … |
| maximal quotient of | #10709303, #10709359, #10709478, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3465);