Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#5398 |
267 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 267 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 22 points:
(3,4,6)(7,9,16,20,11,18,10,17)(8,12,19,22,14,21,13,15);(4,5)(7,8,11,14)(9,15,18,22)(10,19,16,13)(12,20,21,17);(1,2)44 conjugacy classes — view the full character table.
| maximal subgroup of | #11711568, #11711573, #11711599, … |
| maximal normal subgroup of | #11711568, #11711573, #11711599, … |
| maximal quotient of | C2×#73015, C2×#73014, C2×#73016, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18010);