Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×#4907 |
| Fitting | C2×C3×M32 ⋊ C2 |
| Sylow | C3 ⋊ C2×#504 |
368 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 213 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)(6,8,9,17,10,18,19,30,11,16,20,28,21,29,31,36)(7,13,14,25,15,26,27,35,12,22,23,32,24,33,34,37);(1,2)(7,12)(8,16)(14,23)(15,24)(17,28)(18,29)(27,34)(30,36);(4,5)(6,7)(8,13)(9,14)(10,15)(11,12)(16,22)(17,25)(18,26)(19,27)(20,23)(21,24)(28,32)(29,33)(30,35)(31,34)(36,37);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10710282, #10710287, #10710289, … |
| maximal normal subgroup of | #10710282, #10710287, #10710289, … |
| maximal quotient of | C2×#69072, C2×#71419, C4×#4907, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14582);