Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C97 ⋊ #347 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C4×#87604 |
| commutator | C4×C97 | C42 |
| Frattini | C2×C4 | C2×#87604 |
| Fitting | C2×C8×C97 | C4 |
| socle | C2×C97 | #97 |
| hypercenter | C2×C8 | #87604 |
| hypocenter | C97 | #347 |
| LCS | G ▷ C4×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ C2×C8 | |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=c,b^2=d,c^2=e,e^2=f,b^a=be,d^a=df,g^a=g^22,c^b=cf,g^b=g^96,g^c=g^96406 conjugacy classes — view the full character table.
| maximal subgroup of | #27157953, C2×#20261628, #27157958, … |
| maximal normal subgroup of | #27157953, C2×#20261628, #27157958, … |
| maximal quotient of | #27156654, #27156778, C2×#20261628 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1442);