Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×C4×D36 |
| Fitting | C2×C42×C9 ⋊ C2 |
| Sylow | C9 ⋊ C2×C4×D4 |
639 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 639 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #11773805, #11773941, C2×#10588162, … |
| maximal normal subgroup of | #11773805, #11773941, C2×#10588162, … |
| maximal quotient of | C2×C4×(C2×D9)⋊C4, C2×C4×C4⋊Dic9, C42×D36, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1457);