Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of #14268487 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C52 ⋊ C23 |
| Sylow | C52 ⋊ C2×D32 |
| Sylow | C32 ⋊ C2×D52 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C52 | C23 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 | |
336 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 30 |
Polycyclic presentation:
2^3,3^2,5^2|d^a=d^2,f^a=f^4,f^b=f^4,g^b=g^4,d^c=d^2,e^c=e^278 conjugacy classes — view the full character table.
| maximal subgroup of | #72210392, C3×#14268487, #72222479, … |
| maximal normal subgroup of | #72210392, C3×#14268487, D32×D52, … |
| maximal quotient of | C3×#14268487, #72222479, #72222509, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 681);