Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C97 ⋊ #383 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D97 |
| commutator | C22×C97 | C22×C4 |
| Fitting | #95×C97 | C2 |
| socle | C23×C97 | C23 |
| hypercenter | #95 | D97 |
| hypocenter | C97 | #383 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C23 ◁ #95 | |
138 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=f,b^2=de,c^2=d,b^a=bd,c^a=ce,g^c=g^96988 conjugacy classes — view the full character table.
| maximal subgroup of | #27140281, #27140285, #27140310, … |
| maximal normal subgroup of | #27140281, #27140285, #27140310, … |
| maximal quotient of | #27139960, #27139961, #27139962, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 416);