Finite Group DatabasebetaFinite Group Databasebeta| order | 31300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#11929411 |
| Fitting, Hall | C25×C313 ⋊ C4 |
| derived, Sylow | C313 ⋊ C4×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #11929411 |
| commutator, hypocenter | C313 | C4×C25 |
| Frattini | C5 | C5×#11929411 |
| Fitting | C25×C313 | C4 |
| socle | C5×C313 | C4×C5 |
| prime radical, cosocle | C5×D313 | C2×C5 |
| LCS | G ▷ C313 | |
| UCS | C1 ◁ C25 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7825 |
2050 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31300, 6);