Finite Group DatabasebetaFinite Group Databasebeta| order | 15100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×#16836849⋊C2 |
| unambiguous semidirect product | #16836849⋊C22 |
| unambiguous semidirect product | (C2×#16836849)⋊C2 |
| derived, Sylow | C151 ⋊ C22×C25 |
| Hall | #16836849 ⋊ C22 |
| Hall | C2×D151 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D151⋊C5 |
| commutator, hypocenter | C151 | C22×C25 |
| Frattini | C5 | C2×D151⋊C5 |
| Fitting, socle | C2×C5×C151 | C2×C5 |
| prime radical | C2×C5×D151 | C5 |
| cosocle | C5×C151 | C22×C5 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C2×C5 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7550 |
250 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15100, 8);