Finite Group DatabasebetaFinite Group Databasebeta| order | 24115 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7×C13 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C5×C7×C53 ⋊ C13 |
| derived, Sylow | C53 ⋊ C5×C7×C13 |
| Hall | C7×C53 ⋊ C5×C13 |
| Hall | C5×C53 ⋊ C7×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | C53⋊C13 |
| commutator, cosocle, hypocenter | C53 | C5×C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C53 | C13 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C5×C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1855 |
595 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24115, 2);