Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4918 |
| Fitting | C2×C3×Q32 ⋊ C2 |
| Sylow | C3 ⋊ C2×#510 |
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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:
(1,2)(3,4,5)(6,8,11,16)(7,12,15,27)(9,21,24,37)(10,26,22,19)(13,31,32,36)(14,33,25,29)(17,35,34,20)(18,30,28,23);(1,2)(6,7,11,15)(8,17,16,34)(9,20,24,35)(10,25,22,14)(12,28,27,18)(13,30,32,23)(19,36,26,31)(21,33,37,29);(4,5)(8,16)(12,27)(17,34)(18,28)(19,26)(21,37)(29,33)(31,36);(1,2)54 conjugacy classes — view the full character table.
| maximal subgroup of | #10948513, C4×#4918, #10948535, … |
| maximal normal subgroup of | #10948513, C4×#4918, #10948535, … |
| maximal quotient of | C2×#69222, C2×#69221, C2×#69326, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14603);