Finite Group DatabasebetaFinite Group Databasebeta| order | 11025 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C5×C7 |
| unambiguous semidirect product | C52⋊#89205 |
| derived, Hall | C52×C72 ⋊ C9 |
| Sylow | C72 ⋊ C52⋊C9 |
| Sylow | C52 ⋊ #89205 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C52⋊#3862 |
| commutator, hypocenter | C52×C72 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C52×C72 | C3 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
3,5^2,7^2,3|a^3=f,b^a=bc^2,c^a=bc^3,d^a=d^2,e^a=e^41233 conjugacy classes. The character table is too large to display.
| derived subgroup of | #36347818 |
| maximal subgroup of | #36347818, #36347824, #36347826, … |
| maximal normal subgroup of | #36347818, #36347824, #36347826, … |
| maximal quotient of | C2×C52⋊#89205 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11025, 30);