Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×M32 ⋊ C2 |
| Sylow | C3 ⋊ #2113 |
228 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3)(10,18)(14,24)(19,30)(20,31)(25,34)(26,35)(32,38)(36,39);(2,3)(5,7)(8,10)(9,14)(11,19)(12,20)(13,18)(15,25)(16,26)(17,24)(21,32)(22,30)(23,31)(27,36)(28,34)(29,35)(33,38)(37,39);(2,3)(4,5)(6,7)(8,9,11,15,12,16,21,27,13,17,22,28,23,29,33,37)(10,14,19,25,20,26,32,36,18,24,30,34,31,35,38,39)Polycyclic presentation:
2^7,3|a^2=e,e^2=f,f^2=g,b^a=bd,h^a=h^2,c^b=cg,h^b=h^296 conjugacy classes — view the full character table.
| maximal subgroup of | #10682531, #10710636, #10710640, … |
| maximal normal subgroup of | #10682531, #10710636, #10710640, … |
| maximal quotient of | #10704253, #10704325, #10704394, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4008);