Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#63947 |
| Sylow | C32 ⋊ C2×#135 |
562 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#63947, #11860023, #11860214, … |
| maximal normal subgroup of | C4×#63947, #11860023, #11860214, … |
| maximal quotient of | C2×#10590608, C2×#10591556, C2×#10590572, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7214);