Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #2117 |
220 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 220 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) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3)(5,12)(11,26)(13,15)(14,28)(16,29)(27,31)(30,32)(33,35);(4,6)(5,11)(7,20)(8,22)(9,17)(10,19)(12,26)(13,29)(14,31)(15,16)(18,24)(21,34)(23,25)(27,28)(30,33)(32,35);(2,3)(4,5,8,14,9,15,23,32,10,12,24,28,7,13,21,30)(6,16,18,33,17,26,34,31,19,29,22,35,20,11,25,27)Polycyclic presentation:
2^7,3|a^2=e,d^2=g,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^2,d^b=dg,e^b=eg84 conjugacy classes — view the full character table.
| maximal subgroup of | #10710261, #10710263, #10710312, … |
| maximal normal subgroup of | #10710261, #10710263, #10710312, … |
| maximal quotient of | #10704259, #10704262, #10704331, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4582);