Finite Group DatabasebetaFinite Group Databasebeta| order | 3104 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C97 ⋊ C2 |
| Sylow | C97 ⋊ #123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D97 |
| commutator, socle, cosocle | C22×C97 | C23 |
| Fitting | C22⋊C4×C97 | C2 |
| prime radical | C2×C22⋊D97 | C2 |
| hypercenter | C22⋊C4 | D97 |
| hypocenter | C97 | #123 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1552 |
Polycyclic presentation:
2^5,97|c^2=d,b^a=bd,c^a=ce,f^b=f^96494 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3104, 128);