Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#4683 |
| Sylow | C3 ⋊ C2×#499 |
360 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 181 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) = 384 |
A minimal faithful permutation representation — 4 generators on 29 points:
(3,4,5)(14,16,17,23,18,24,26,28)(15,20,21,22,19,27,25,29);(1,2)(6,8,9,13)(7,10,11,12)(15,19)(20,27)(21,25)(22,29);(4,5)(6,7,9,11)(8,12,13,10)(14,15,18,19)(16,22,24,29)(17,25,26,21)(20,28,27,23);(1,2)108 conjugacy classes — view the full character table.
| maximal subgroup of | #10694733, #10694735, #10694757, … |
| maximal normal subgroup of | #10694733, #10694735, #10694757, … |
| maximal quotient of | C2×#69766, C2×#69769, C2×#69770, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11016);