Finite Group DatabasebetaFinite Group Databasebeta| order | 24608 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4⋊C4×C769 ⋊ C2 |
| Sylow | C769 ⋊ #126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D769 |
| commutator, socle, cosocle | C22×C769 | C23 |
| Fitting | C4⋊C4×C769 | C2 |
| prime radical | C22×D769 | C22 |
| hypercenter | C4⋊C4 | D769 |
| hypocenter | C769 | #126 |
| LCS | G ▷ C22×C769 ▷ C769 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12304 |
Polycyclic presentation:
2^5,769|b^2=de,c^2=d,b^a=bd,c^a=ce,f^a=f^768,f^c=f^7683854 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24608, 141);