Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C32 ⋊ C2×C4×Q8 |
642 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=f,b^2=f,c^2=e,d^2=ef,h^a=h^2,g^b=g^2,d^c=de90 conjugacy classes — view the full character table.
| maximal subgroup of | #11786902, #11786999, #11787509, … |
| maximal normal subgroup of | #11786902, #11786999, #11787509, … |
| maximal quotient of | #11800733, C4⋊C4×#624, #11800841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6245);