Finite Group DatabasebetaFinite Group Databasebeta| order | 21525 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C41 · Schur multiplier (H2) = C5 |
| Fitting, socle, Hall | C52×C7×C41 ⋊ C3 |
| derived, Hall | C52×C7 ⋊ C3×C41 |
| Hall | C52×C41 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C41 ⋊ C52⋊C3 |
| Sylow | C52 ⋊ ΓL(1,𝔽8)×C41 |
| Sylow | C7 ⋊ C41×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | C7⋊(C52⋊C3) |
| commutator, cosocle, hypocenter | C52×C7 | C3×C41 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C41 | C3 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C41 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4305 |
2501 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21525, 9);