Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4755 |
| Fitting | C2×C3×#101 ⋊ C2 |
| Sylow | C3 ⋊ C2×#473 |
448 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 37 points:
(3,4,5)(6,9,11,21)(7,13,15,29)(8,16,18,33)(10,22,23,20)(12,24,26,27)(14,19,30,28)(17,34,35,32)(25,36,37,31);(6,8,10,17,11,18,23,35)(7,12,14,25,15,26,30,37)(9,16,20,32,21,33,22,34)(13,27,28,36,29,24,19,31);(1,2)(4,5)(6,7)(8,12)(9,19)(10,14)(11,15)(13,20)(16,31)(17,25)(18,26)(21,28)(22,29)(23,30)(24,34)(27,32)(33,36)(35,37);(1,2)54 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4755, #10802077, #10802098, … |
| maximal normal subgroup of | C4×#4755, #10802077, #10802098, … |
| maximal quotient of | C2×#68441, C2×#68443, C2×#68444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11287);