Finite Group DatabasebetaFinite Group Databasebeta| order | 24644 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C101 · Schur multiplier (H2) = C1 |
| direct product | C101×#6923 |
| Fitting, socle, Hall | C61×C101 ⋊ C4 |
| derived, Sylow | C61 ⋊ C4×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C101 | #6923 |
| commutator, hypocenter | C61 | C4×C101 |
| Frattini | C1 | G |
| Fitting, socle | C61×C101 | C4 |
| prime radical | C101×D61 | C2 |
| cosocle | D61 | C2×C101 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C101 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6161 |
1919 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24644, 7);