Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C97 ⋊ #408 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#87604 |
| commutator, socle | C22×C97 | C22×C4 |
| Fitting | C2×Q8×C97 | C4 |
| hypercenter | C2×Q8 | #87604 |
| hypocenter | C97 | #408 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
158 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=e,e^2=f,b^a=bd,g^a=g^22,c^b=cf,g^b=g^96,g^c=g^96,g^e=g^96268 conjugacy classes — view the full character table.
| maximal subgroup of | #27156838, #27157585, #27157694, … |
| maximal normal subgroup of | #27156838, #27157585, #27157694, … |
| maximal quotient of | #27157004, #27157007, #27157010, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1524);