Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #2166 |
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 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:
(2,3)(5,11,12,14)(6,16)(7,20)(10,23,15,26)(13,30,28,27)(18,31)(21,25)(24,35,29,34);(1,2,3)(4,6)(5,10)(7,19)(8,18)(9,16)(11,26)(12,15)(13,29)(14,23)(17,20)(21,33)(22,31)(24,28)(25,32)(27,34)(30,35);(4,5,7,13,8,14,21,30,9,12,20,28,22,11,25,27)(6,15,17,29,18,26,32,35,16,10,19,24,31,23,33,34)Polycyclic presentation:
2^7,3|a^2=e,c^2=d,e^2=f,f^2=g,b^a=bd,c^a=cf,d^a=dg,c^b=cg,e^b=eg,e^c=eg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | #10704684, #10704686, #10704688, … |
| maximal normal subgroup of | #10704684, #10704686, #10704688, … |
| maximal quotient of | #10710206, #10710259, #10710524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1691);