Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C97 ⋊ #346 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×#11715906 |
| commutator | C2×C97 | C4×C8 |
| Fitting | C2×C4×C97 | C8 |
| socle | C22×C97 | C2×C8 |
| hypercenter | C2×C4 | #11715906 |
| hypocenter | C97 | #346 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=c,b^2=d,c^2=e,e^2=f,b^a=bf,g^a=g^64,g^c=g^22,g^e=g^96136 conjugacy classes — view the full character table.
| maximal subgroup of | #27158780, #27158781, #27158792, … |
| maximal normal subgroup of | #27158780, #27158781, #27158792, … |
| maximal quotient of | #27158752, #27158754, #27158806, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1643);