Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#5430 |
297 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 297 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 3 generators on 34 points:
(3,6,18)(4,21,26,9,11,33)(5,29,31,14,15,32)(8,19,20)(10,27,34,13,23,28)(12,22)(16,30)(24,25);(3,4,8,13)(5,9,14,10)(6,12,19,25)(7,11,17,27)(15,22,29,24)(16,21,30,23)(18,28,20,26)(31,34,32,33);(1,2)34 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#5430, #11712835, #11713088, … |
| maximal normal subgroup of | C4×#5430, #11712835, #11713088, … |
| maximal quotient of | C2×#73087, C2×#73085, C2×#73095, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18107);