Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#5423 |
313 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 313 conjugacy classes of subgroups — too many to draw. Only its 62 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:
(1,2)(3,6,17)(4,21,25,9,11,26)(5,13,28)(8,18,19)(10,31,33,20,23,34)(12,22)(15,29,30)(24,32);(3,4,5,10,8,9,15,20)(6,12,13,24,18,22,29,32)(7,11,14,23,16,21,27,31)(17,26,28,34,19,25,30,33);(1,2)52 conjugacy classes — view the full character table.
| maximal subgroup of | #11711305, #11711306, #11711308, … |
| maximal normal subgroup of | #11711305, #11711306, #11711308, … |
| maximal quotient of | C2×#73056, C2×#73071, #11711787, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18085);