Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#5137 |
| Sylow | C3 ⋊ C2×#470 |
492 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,2)(3,4,5)(6,7)(8,9)(12,20)(15,24)(18,25)(21,23);(1,2)(10,12,19,23,14,20,13,21)(11,15,22,25,17,24,16,18);(4,5)(7,9)(10,11,14,17)(12,18,20,25)(13,22,19,16)(15,23,24,21);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#67482, C2×#67536, C2×#67484, … |
| maximal normal subgroup of | C2×#67482, C2×#67536, C2×#67484, … |
| maximal quotient of | C2×#70871, C2×#70874, C2×#70876, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16351);