Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×M32 ⋊ C2 |
| Sylow | C3 ⋊ #2148 |
220 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 81 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)(4,7,9,21)(5,11,14,13)(6,16,19,18)(8,20,24,33)(10,25,27,26)(12,28,30,22)(15,31,32,29)(17,23,35,34);(2,3)(4,6)(5,10)(7,16)(8,23)(9,19)(11,25)(12,29)(13,26)(14,27)(15,28)(17,33)(18,21)(20,35)(22,32)(24,34)(30,31);(2,3)(4,5,7,11,9,14,21,13)(6,15,18,29,19,32,16,31)(8,22,20,12,24,28,33,30)(10,23,26,17,27,34,25,35)Polycyclic presentation:
2^7,3|a^2=e,c^2=g,d^2=f,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^2,d^b=dfg,e^b=eg,f^b=fg,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10710451, #10710452, #10710486, … |
| maximal normal subgroup of | #10710451, #10710452, #10710486, … |
| maximal quotient of | #10704954, #10704959, #10705190, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4018);