Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#5672 |
| Sylow | C3 ⋊ C2×#563 |
1024 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1024 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 5 generators on 29 points:
(1,2)(3,4,5)(6,8)(7,11)(9,12)(10,13)(14,18,19,26)(15,21,22,29)(16,23,17,25)(20,27,24,28);(6,7)(8,11)(9,10)(12,13)(14,17,19,16)(15,20,22,24)(18,23,26,25)(21,28,29,27);(7,10)(11,13)(14,16)(15,20)(17,19)(18,25)(21,28)(22,24)(23,26)(27,29);(4,5)(8,12)(11,13)(14,15,19,22)(16,20,17,24)(18,21,26,29)(23,27,25,28);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10687632, #10687635, #10711014, … |
| maximal normal subgroup of | #10687632, #10687635, #10711014, … |
| maximal quotient of | C2×#76309, C2×#75491, C2×#82957, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18643);