Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1858 |
252 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3)(4,7)(5,12)(6,16)(8,23)(9,19)(10,20)(11,24)(13,28)(14,29)(15,30)(17,34)(18,33)(21,27)(22,32)(25,35)(26,31);(2,3)(4,6,9,17,10,18,8,22)(5,11,13,26,14,25,21,15)(7,16,19,34,20,33,23,32)(12,24,28,31,29,35,27,30);(4,5,9,13,10,14,8,21)(6,15,17,11,18,26,22,25)(7,12,19,28,20,29,23,27)(16,31,34,35,33,30,32,24)Polycyclic presentation:
2^7,3|a^2=f,b^2=f,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,d^b=dg,e^b=eg,h^b=h^2,d^c=dg60 conjugacy classes — view the full character table.
| maximal subgroup of | #10682618, #10682620, #10682621, … |
| maximal normal subgroup of | #10682618, #10682620, #10682621, … |
| maximal quotient of | #10689048, #10689053, #10689058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2577);