Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#4497 |
| Fitting | C2×C3×#108 ⋊ C2 |
| Sylow | C3 ⋊ C2×#359 |
224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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 — 3 generators on 37 points:
(3,4,5)(6,8,9,18,11,21,23,20)(7,12,13,27,16,28,15,32)(10,25,22,19,26,34,37,35)(14,30,29,33,31,36,24,17);(4,5)(6,7)(8,17)(9,13)(10,24)(11,16)(12,19)(14,22)(15,23)(18,30)(20,36)(21,33)(25,32)(26,29)(27,34)(28,35)(31,37);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10710410, C4×#4497, #10710415, … |
| maximal normal subgroup of | #10710410, C4×#4497, #10710415, … |
| maximal quotient of | C2×#67471, C2×#67472, #10704925, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3265);