Finite Group DatabasebetaFinite Group Databasebeta| order | 3104 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D8×C97 ⋊ C2 |
| Sylow | C97 ⋊ D16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #13095496 |
| commutator, cosocle | C8×C97 | C22 |
| Frattini | C8 | C2×D97 |
| Fitting | D8×C97 | C2 |
| socle | C2×C97 | D8 |
| hypercenter | D8 | D97 |
| hypocenter | C97 | D16 |
| LCS | G ▷ C8×C97 ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ D8 | |
28 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 1552 |
Polycyclic presentation:
2^5,97|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,c^b=cd,d^b=de,f^b=f^96347 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3104, 87);