Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4537 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1296 |
188 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 105 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) = 384 |
A minimal faithful permutation representation — 2 generators on 23 points:
(2,3)(8,9,10,13,11,12,14,15)(17,20)(18,23)(21,22);(1,2,3)(4,5,6,7)(9,12)(10,14)(16,17)(18,20)(19,22)(21,23)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,c^b=cg,h^b=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | #10682739, #10682740, #10682817, … |
| maximal normal subgroup of | #10682739, #10682740, #10682817, … |
| maximal quotient of | #10681738, #10681754, #10681776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 210);