Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4451 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#4465 |
| Sylow | C3 ⋊ C2×#330 |
232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 85 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) = 384 |
A minimal faithful permutation representation — 3 generators on 21 points:
(3,4,5)(7,10,11,12)(14,16,17,20,19,21,18,15);(4,5)(6,7)(8,10)(9,11)(12,13)(14,15,19,20)(16,18,21,17);(1,2)78 conjugacy classes — view the full character table.
| maximal subgroup of | #10686104, C4×#4465, #10686112, … |
| maximal normal subgroup of | #10686104, C4×#4465, #10686112, … |
| maximal quotient of | C2×#67477, C2×#67478, #10683158, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2376);