Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#5518 |
| Sylow | C3 ⋊ C2×#541 |
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 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)(7,10)(9,12)(11,13)(14,17,18,25)(15,20,21,27)(16,23,24,29)(19,26,22,28);(6,7,9,11)(8,10,12,13)(17,25)(20,27)(23,29)(26,28);(14,16,18,24)(15,19,21,22)(17,23,25,29)(20,26,27,28);(4,5)(8,12)(10,13)(14,15,18,21)(16,22,24,19)(17,20,25,27)(23,28,29,26);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10686624, #10687701, #10687703, … |
| maximal normal subgroup of | #10686624, #10687701, #10687703, … |
| maximal quotient of | C2×#82231, C2×#73386, C2×#82235, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18299);