Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#4477 |
| Fitting | C2×C3×#101 ⋊ C2 |
| Sylow | C3 ⋊ C2×#355 |
260 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 69 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 — 3 generators on 21 points:
(3,4,5)(6,7,8,12,10,13,15,21)(9,11,17,18,16,19,14,20);(4,5)(7,11)(9,16)(12,20)(13,19)(14,17)(18,21);(1,2)48 conjugacy classes — view the full character table.
| maximal subgroup of | #10710364, C4×#4477, #10710376, … |
| maximal normal subgroup of | #10710364, C4×#4477, #10710376, … |
| maximal quotient of | C2×#67454, C2×#67452, #10704459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2703);