Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C97 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#87604 |
| commutator, socle | C2×C97 | C22×C8 |
| Fitting | M16×C97 | C4 |
| hypercenter | M16 | #87604 |
| hypocenter | C97 | #504 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ M16 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=d,d^2=e,e^2=f,g^a=g^22,c^b=cf,g^b=g^96,g^d=g^96280 conjugacy classes — view the full character table.
| maximal subgroup of | #27158124, #27158125, #27158127, … |
| maximal normal subgroup of | #27158124, #27158125, #27158127, … |
| maximal quotient of | #27157946, #27157947, #27157967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1608);