Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #2398 |
568 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 161 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:
(1,2,3)(16,18,19,22)(17,21,20,23);(5,7)(9,13)(10,15)(17,20)(21,23);(2,3)(4,5)(6,7)(8,10,11,15)(9,12,13,14);(8,9,11,13)(10,14,15,12)(16,17)(18,21)(19,20)(22,23)Polycyclic presentation:
2^7,3|a^2=e,b^2=e,d^2=ef,b^a=be,c^a=cf,c^b=cg,h^b=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10690254, #10690256, #10690268, … |
| maximal normal subgroup of | #10690254, #10690256, #10690268, … |
| maximal quotient of | #10716890, #10716925, #10716944, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14924);