Finite Group DatabasebetaFinite Group Databasebeta| order | 24608 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C769 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #20259679 |
| commutator, hypocenter | C769 | C32 |
| Fitting | C4×C769 | C8 |
| socle, prime radical | C2×C769 | C16 |
| cosocle | #27134384 | C2 |
| LCS | G ▷ C769 | |
| UCS | C1 ◁ C4 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24608 |
Polycyclic presentation:
2^5,769|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^40,f^b=f^62,f^c=f^768416 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24608, 236);