Finite Group DatabasebetaFinite Group Databasebeta| order | 24990 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C7 |
| direct product | C5×D17×#3862 |
| unambiguous semidirect product | C17⋊(C2×C5×#3862) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D17×#3862 |
| commutator, cosocle, hypocenter | C72×C17 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C17 | C2×C3 |
| LCS | G ▷ C72×C17 | |
| UCS | C1 ◁ C5 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1785 |
950 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24990, 42);