Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#13095514 |
| Sylow | C97 ⋊ C4⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×#87604 |
| commutator | C2×C97 | C2×C16 |
| Fitting | C42×C97 | C4 |
| socle | C22×C97 | C2×C8 |
| hypercenter | C42 | #87604 |
| hypocenter | C97 | C4⋊C16 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
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^22,g^d=g^96424 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#13095514, #27156687, #27156688, … |
| maximal normal subgroup of | D4⋊#13095514, #27156687, #27156688, … |
| maximal quotient of | #27156758, #27156765, #27156774, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1469);