Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #3788 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C3×C4 |
| direct product | C4×C22⋊#157 |
| Fitting | C22×C32×C4 ⋊ C4 |
| Sylow | C32 ⋊ C4×C22⋊C4 |
494 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #11770840, #11770841, #11770848, … |
| maximal normal subgroup of | #11770840, #11770841, #11770848, … |
| maximal quotient of | C4×#63781, #11773160, #11773184, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5692);