Finite Group DatabasebetaFinite Group Databasebeta| order | 23648 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C739⋊#95 |
| Sylow | C739 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D739 |
| commutator | C2×C739 | C42 |
| Fitting | C22×C4×C739 | C2 |
| socle, prime radical, cosocle | C23×C739 | C22 |
| hypercenter | C22×C4 | D739 |
| hypocenter | C739 | #95 |
| LCS | G ▷ C2×C739 ▷ C739 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23648 |
Polycyclic presentation:
2^5,739|a^2=d,b^2=e,b^a=bc,f^b=f^7385924 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23648, 53);