Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#21440600 |
| Fitting | C2×C4⋊C4×C241 ⋊ C2 |
| Sylow | C241 ⋊ C2×#117 |
330 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7712 |
2440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44505758, #44505778, #44507160, … |
| maximal normal subgroup of | #44505758, #44505778, #44507160, … |
| maximal quotient of | C2×#29507562, C2×#29507564, C2×C4⋊C4×Dic241, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 1004);