Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#4893 |
| Fitting | C2×C3×#108 ⋊ C2 |
| Sylow | C3 ⋊ C2×#430 |
460 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 213 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 — 4 generators on 21 points:
(3,4,5)(6,8,9,17,11,18,10,19)(7,13,14,16,12,20,15,21);(6,7,10,15,11,12,9,14)(8,16,17,20,18,21,19,13);(1,2)(4,5)(7,12)(13,20)(14,15)(16,21);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10711513, #10711516, #10711518, … |
| maximal normal subgroup of | #10711513, #10711516, #10711518, … |
| maximal quotient of | C2×#68528, C2×#68568, #10764169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11827);