Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C97 · Schur multiplier (H2) = C25 |
| direct product | C2×C4⋊Q8×C97 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C97 | C23 |
| commutator, Frattini, cosocle | C22 | C24×C97 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C97 ◁ G | |
290 conjugacy classes of subgroups.
2716 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#332×C97, C2×#333×C97, C97×#1546, … |
| maximal normal subgroup of | C2×#332×C97, C2×#333×C97, C97×#1546, … |
| maximal quotient of | C2×#384×C97, C2×#389×C97, C2×#391×C97, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 212);