Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×D4×C3⋊Dic3 |
| Sylow | C32 ⋊ C2×C4×D4 |
1278 conjugacy classes of subgroups; only the 527 normal subgroups are shown.
This group has 1278 conjugacy classes of subgroups — too many to draw. Only its 527 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #11773788, #11773812, #11773925, … |
| maximal normal subgroup of | #11773788, #11773812, #11773925, … |
| maximal quotient of | C2×C22⋊C4×C3⋊Dic3, C2×C4⋊C4×C3⋊Dic3, C4×D4×C3⋊Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8148);