Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C8×C97 ⋊ C4 |
| Sylow | C97 ⋊ #340 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C4⋊#87604 |
| commutator | C4×C97 | C42 |
| Frattini | C2×C4 | C2×#87604 |
| Fitting | C2×C8×C97 | C4 |
| socle | C22×C97 | C4⋊C4 |
| hypercenter | C2×C8 | #87604 |
| hypocenter | C97 | #340 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 | |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=d,b^2=e,c^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^22,g^d=g^96412 conjugacy classes — view the full character table.
| maximal subgroup of | #27156722, #27156723, #27156724, … |
| maximal normal subgroup of | #27156722, #27156723, #27156724, … |
| maximal quotient of | #27156566, #27156571, #27156590, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1423);