Finite Group DatabasebetaFinite Group Databasebeta| order | 24608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C769 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #15690484 |
| commutator, hypocenter | C769 | C2×C16 |
| Frattini | C4 | C2×#15690484 |
| Fitting | C8×C769 | C4 |
| socle | C2×C769 | C2×C8 |
| prime radical | C2×D769 | C8 |
| cosocle | #20259670 | C22 |
| LCS | G ▷ C769 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12304 |
Polycyclic presentation:
2^5,769|a^2=c,c^2=d,d^2=e,f^a=f^62,f^b=f^768,f^c=f^7681568 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24608, 219);