Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C97 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#11715906 |
| commutator, socle | C2×C97 | C22×C8 |
| Fitting | Q8×C97 | C8 |
| hypercenter | Q8 | #11715906 |
| hypocenter | C97 | #504 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=d,d^2=e,e^2=f,g^a=g^64,c^b=cf,g^b=g^96,g^c=g^96,g^d=g^22,g^e=g^96100 conjugacy classes — view the full character table.
| maximal subgroup of | #27158954, #27158955, #27158956, … |
| maximal normal subgroup of | #27158954, #27158955, #27158956, … |
| maximal quotient of | #27158898, #27158908, #27158928, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1671);