Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×#135 ⋊ C2 |
| Sylow | C3 ⋊ #3280 |
526 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 131 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)(9,14)(10,17)(11,21)(13,16)(18,19)(22,23);(2,3)(5,7);(8,10)(9,13)(11,17)(12,19)(14,22)(15,23)(16,20)(18,21);(4,5)(6,7)(8,9,12,14)(10,16,19,23)(11,20,21,15)(13,17,22,18)Polycyclic presentation:
2^7,3|a^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,h^c=h^2,e^d=eg63 conjugacy classes — view the full character table.
| maximal subgroup of | #10951639, #10951648, #10951669, … |
| maximal normal subgroup of | #10951639, #10951648, #10951669, … |
| maximal quotient of | #10784775, #10784790, #10784805, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16494);