Finite Group DatabasebetaFinite Group Databasebeta| order | 24608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C769 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#20259679 |
| commutator, socle | C2×C769 | C2×C8 |
| Fitting, prime radical | C22×C769 | C8 |
| cosocle | #20259677 | C22 |
| hypercenter | C22 | #20259679 |
| hypocenter | C769 | M32 |
| LCS | G ▷ C2×C769 ▷ C769 | |
| UCS | C1 ◁ C2 ◁ C22 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12304 |
Polycyclic presentation:
2^5,769|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^40,f^c=f^62,f^d=f^768404 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24608, 242);