Finite Group DatabasebetaFinite Group Databasebeta| order | 30900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C5⋊(D103⋊C3))⋊D5 |
| unambiguous semidirect product | ((C5⋊D5)⋊D103)⋊C3 |
| Fitting, socle, derived, Hall | C52×C103 ⋊ C22×C3 |
| Hall | (C5⋊D5)⋊D103 ⋊ C3 |
| Hall | C52×C103⋊C3 ⋊ C22 |
| Hall | C103⋊C3 ⋊ D52 |
| Sylow | C103 ⋊ C3×D52 |
| Sylow | C52 ⋊ C2×D103⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C103 | C22×C3 |
| LCS | G ▷ C52×C103 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1030 |
Polycyclic presentation:
2^2,3,5^2,103|d^a=d^4,f^a=f^102,d^b=d^4,e^b=e^4,f^c=f^46286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30900, 88);