Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C22×C3×H(3,𝔽3) ⋊ C22 |
| Sylow | C3×H(3,𝔽3) ⋊ C2×D4 |
697 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 697 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^4,3^4|e^a=e^2,f^a=f^2,h^a=h^2,c^b=cd,g^b=g^2,h^b=h^2,g^f=gh63 conjugacy classes — view the full character table.
| maximal subgroup of | #72219712, #72219727, #72219731, … |
| maximal normal subgroup of | #72219727, #72219731, D4×((C3⋊D3)⋊C3)⋊D3, … |
| maximal quotient of | #72259905, #72259972, C3×#13048731 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2449);