Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C97 ⋊ #456 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #15690779 |
| commutator | C2×C4×C97 | C23 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | 2−1+4×C97 | C2 |
| socle | C2×C97 | #120 |
| hypercenter | 2−1+4 | D97 |
| hypocenter | C97 | #456 |
| LCS | G ▷ C2×C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ 2−1+4 | |
142 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=f,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^96,d^b=df,e^b=ef,d^c=df832 conjugacy classes — view the full character table.
| maximal subgroup of | #27143755, #27143756, #27143760, … |
| maximal normal subgroup of | #27143755, #27143756, #27143760, … |
| maximal quotient of | #27140699, #27140705, #27140710, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 732);