Finite Group DatabasebetaFinite Group Databasebeta| order | 25215 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C41 |
| direct product | C3×#22554263 |
| Fitting, socle, Hall | C3×C412 ⋊ C5 |
| derived, Sylow | C412 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #22554263 |
| commutator, cosocle, hypocenter | C412 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C412 | C5 |
| LCS | G ▷ C412 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 615 |
1023 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25215, 8);