Finite Group DatabasebetaFinite Group Databasebeta| order | 23484 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #26044105⋊C2 |
| unambiguous semidirect product | #26044109⋊C2 |
| unambiguous semidirect product | #26044113⋊C2 |
| Fitting, socle, derived, Hall | C19×C103 ⋊ C22×C3 |
| Hall | D19×D103 ⋊ C3 |
| Hall | #19154536 ⋊ C22 |
| Sylow | C103 ⋊ C2×D19⋊C3 |
| Sylow | C19 ⋊ C2×D103⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C103 | C22×C3 |
| LCS | G ▷ C19×C103 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1957 |
Polycyclic presentation:
2^2,3,19,103|e^a=e^102,d^b=d^18,d^c=d^7,e^c=e^56205 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23484, 27);