Finite Group DatabasebetaFinite Group Databasebeta| order | 3104 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C97 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #87604 |
| commutator, hypocenter | C97 | C2×C16 |
| Frattini | C4 | C2×#87604 |
| Fitting | C8×C97 | C4 |
| socle | C2×C97 | C2×C8 |
| prime radical | C2×D97 | C8 |
| cosocle | #11715895 | C22 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1552 |
Polycyclic presentation:
2^5,97|a^2=c,c^2=d,d^2=e,f^a=f^22,f^b=f^96,f^c=f^96224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3104, 219);