Finite Group DatabasebetaFinite Group Databasebeta| order | 21700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | D217⋊(C5⋊D5) |
| Fitting, socle, derived, Hall | C52×C7×C31 ⋊ C22 |
| Hall | C52×C31 ⋊ C2×D7 |
| Hall | C7×C31 ⋊ C2×C5⋊D5 |
| Hall | C52×C7 ⋊ C2×D31 |
| Sylow | C31 ⋊ D7×C5⋊D5 |
| Sylow | C52 ⋊ D7×D31 |
| Sylow | C7 ⋊ C5⋊D5×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7×C31 | C22 |
| LCS | G ▷ C52×C7×C31 | |
| UCS | C1 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5425 |
Polycyclic presentation:
2^2,5^2,7,31|e^a=e^6,f^a=f^30,c^b=c^4,d^b=d^4,e^b=e^61405 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21700, 107);