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×#4567 |
| Sylow | C3 ⋊ C2×#359 |
224 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 93 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)(7,12)(9,20)(10,21)(13,24)(14,15)(16,26)(17,30)(18,31)(22,34)(23,25)(27,28)(29,36)(32,37)(33,35);(4,5)(6,7,8,13,11,16,19,29)(9,12,17,24,22,26,32,36)(10,23,18,33,21,15,31,28)(14,30,27,34,25,37,35,20);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4567, Dic3×#359, #10710416, … |
| maximal normal subgroup of | C4×#4567, Dic3×#359, #10710416, … |
| maximal quotient of | C2×#67763, C2×#67765, #10704927, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4655);