Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#5798 |
| Sylow | C3 ⋊ C2×#518 |
1920 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1920 conjugacy classes of subgroups — too many to draw. Only its 1077 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 5 generators on 17 points:
(1,2)(3,4,5)(10,12)(11,15)(13,16)(14,17);(10,11)(12,15)(13,14)(16,17);(11,14)(15,17);(4,5)(6,7,8,9)(12,16)(15,17);(1,2)108 conjugacy classes — view the full character table.
| maximal subgroup of | #10700504, #10700507, #10700529, … |
| maximal normal subgroup of | #10700504, #10700507, #10700529, … |
| maximal quotient of | C2×#82083, C2×#82144, C2×#82317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 19804);