Finite Group DatabasebetaFinite Group Databasebeta| order | 3104 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C97 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#11715906 |
| commutator, socle | C2×C97 | C2×C8 |
| Fitting | C4×C97 | C8 |
| prime radical | C2×D97 | C8 |
| cosocle | #11715897 | C22 |
| hypercenter | C4 | #11715906 |
| hypocenter | C97 | M32 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C4 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1552 |
Polycyclic presentation:
2^5,97|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^64,f^b=f^96,f^c=f^22,f^d=f^9668 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3104, 243);