Finite Group DatabasebetaFinite Group Databasebeta| order | 3104 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C97 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C97 | C32 |
| prime radical | D97 | C16 |
| cosocle | #13095525 | C2 |
| LCS | G ▷ C97 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 97 |
Polycyclic presentation:
2^5,97|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^28,f^b=f^8,f^c=f^64,f^d=f^22,f^e=f^9635 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽97), C3×#15690911, #72218953 |
| maximal normal subgroup of | AGL(1,𝔽97), C3×#15690911 |
| maximal quotient of | C3×#15690911, #72218953 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3104, 247);