Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4912 |
| Fitting | C2×C3×D16 ⋊ C2 |
| Sylow | C3 ⋊ C2×#508 |
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 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)(7,13)(9,21)(10,24)(11,19)(12,16)(14,31)(15,33)(17,20)(18,22)(23,35)(25,37)(26,29)(27,30)(28,32)(34,36);(1,2)(7,12)(8,17)(9,20)(10,22)(13,27)(14,30)(16,28)(18,35)(19,34)(21,24)(23,36)(25,32)(29,31)(33,37);(4,5)(6,7)(8,16)(9,14)(10,15)(11,12)(13,19)(17,27)(18,33)(20,32)(21,37)(22,26)(23,25)(24,29)(28,34)(30,36)(31,35);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10715618, #10715623, #10715660, … |
| maximal normal subgroup of | #10715618, #10715623, #10715660, … |
| maximal quotient of | C2×#69188, C2×#69325, C2×Dic3×D16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14593);