Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×#64090 |
| Fitting | C2×C32×C22⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ C2×C4×D4 |
1278 conjugacy classes of subgroups; only the 327 normal subgroups are shown.
This group has 1278 conjugacy classes of subgroups — too many to draw. Only its 327 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 | #11773775, #11773789, #11773794, … |
| maximal normal subgroup of | #11773775, #11773789, #11773794, … |
| maximal quotient of | C2×#10592365, C2×C22⋊C4×C3⋊Dic3, C2×#10592348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7838);