Finite Group DatabasebetaFinite Group Databasebeta| order | 36100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #31825265⋊C2 |
| unambiguous semidirect product | ((C19⋊D19)⋊C25)⋊C2 |
| derived, Hall | C192⋊C25 ⋊ C22 |
| Sylow | C192 ⋊ C2×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C192⋊C25 | C22 |
| Frattini | C5 | #16813380⋊C2 |
| Fitting, socle | C5×C192 | C2×D5 |
| LCS | G ▷ C192⋊C25 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 475 |
Polycyclic presentation:
2^2,5,19^2,5|c^5=f^4,d^a=d^18,e^a=e^18,c^b=c^4f,d^b=d^2e^4,e^b=d^4e^17,f^b=f^4,d^c=d^16e^4,e^c=d^6e^17145 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36100, 47);