Finite Group DatabasebetaFinite Group Databasebeta| order | 24444 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #27132057⋊C2 |
| unambiguous semidirect product | #27132061⋊C2 |
| unambiguous semidirect product | #27132065⋊C2 |
| derived, Hall | C7×C97 ⋊ C22×C9 |
| Hall | #20259170 ⋊ C22 |
| Hall | D7×D97 ⋊ C9 |
| Sylow | C97 ⋊ C2×D7⋊C9 |
| Sylow | C7 ⋊ C2×D97⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #16861350⋊C2 |
| commutator, hypocenter | C7×C97 | C22×C9 |
| Fitting, socle, cosocle | C3×C7×C97 | C22×C3 |
| prime radical | C3×D7×D97 | C3 |
| LCS | G ▷ C7×C97 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6111 |
Polycyclic presentation:
2^2,3,7,97,3|c^3=f,e^a=e^96,d^b=d^6,d^c=d^2,e^c=e^61282 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24444, 30);