Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#5752 |
| Fitting | C2×C3×#131 ⋊ C2 |
| Sylow | C3 ⋊ C2×#576 |
1512 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 5 generators on 21 points:
(3,4,5)(6,8,15,20,10,16,9,14)(7,12,18,21,11,17,13,19);(1,2)(6,7)(8,12)(9,13)(10,11)(14,19)(15,18)(16,17)(20,21);(7,11)(12,17)(13,18)(19,21);(4,5)(8,14)(9,15)(12,19)(13,18)(16,20)(17,21);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10710872, #10710875, #10710882, … |
| maximal normal subgroup of | #10710872, #10710875, #10710882, … |
| maximal quotient of | C2×#83797, C2×#83785, C2×#78560, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 19737);