Finite Group DatabasebetaFinite Group Databasebeta| order | 26176 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #13109888⋊C16 |
| derived, Sylow | C409 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #15692552 |
| commutator, hypocenter | C409 | C4×C16 |
| Frattini | C4 | C2×#15692552 |
| Fitting | C8×C409 | C8 |
| socle | C2×C409 | C4×C8 |
| prime radical | C2×D409 | C2×C8 |
| cosocle | #20266996 | C22 |
| LCS | G ▷ C409 | |
| UCS | C1 ◁ C8 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6544 |
Polycyclic presentation:
2^6,409|a^2=c,b^2=d,c^2=e,e^2=f,g^a=g^31,g^b=g^266,g^c=g^143,g^d=g^408,g^e=g^408472 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26176, 1642);