Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #353 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C97 · Schur multiplier (H2) = C2 |
| direct product | #356×C97 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C97 | #99 |
| commutator | C2×C4 | C2×C4×C97 |
| Frattini, cosocle | C2×Q8 | C22×C97 |
| prime radical | C22×C97 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C97 ◁ C22×C97 ◁ C2×Q8×C97 ◁ G | |
60 conjugacy classes of subgroups.
1261 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C97×#1405, C97×#1410, C97×#1411, … |
| maximal normal subgroup of | C97×#1405, C97×#1410, C97×#1411, … |
| maximal quotient of | C97×#1319, C97×#1325, C97×#1346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 37);