Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#13095525 |
| Fitting | C4×C97 ⋊ C16 |
| Sylow | C97 ⋊ C4⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#13095525 |
| commutator, socle | C2×C97 | C2×C16 |
| Fitting | C4×C97 | C16 |
| hypercenter | C4 | #13095525 |
| hypocenter | C97 | C4⋊C16 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C4 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^a=g^8,g^d=g^64,g^e=g^22,g^f=g^9664 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#13095525, Q8⋊#13095525, #27159000, … |
| maximal normal subgroup of | D4⋊#13095525, Q8⋊#13095525, #27159000, … |
| maximal quotient of | #27159000, #27159001, (C2×#13095525)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1676);