Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting, socle | C3×C52×C37 ⋊ C2×D3 |
| derived, Hall | C3×C37×C52⋊C3 ⋊ C22 |
| Hall | C52×C37 ⋊ C2×C3⋊D3 |
| Hall | C3×C52⋊C3 ⋊ C2×D37 |
| Sylow | C37 ⋊ ((C5⋊D5)⋊C3)⋊D3 |
| Sylow | C52 ⋊ C3⋊D3×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C37×C52⋊C3 | C22 |
| Fitting, socle | C3×C52×C37 | C2×D3 |
| LCS | G ▷ C3×C37×C52⋊C3 | |
| UCS | C1 | |
160 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1665 |
Polycyclic presentation:
2^2,3^2,37,5^2|e^a=e^36,f^a=f^4,g^a=g^4,c^b=c^2,d^b=d^2,f^b=f^4g^2,f^c=f^4g^2,g^c=f^2456 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 555);