Finite Group DatabasebetaFinite Group Databasebeta| order | 6304 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C197 · Schur multiplier (H2) = C22 |
| direct product | C2×Q16×C197 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C197 | D4 |
| commutator, Frattini, cosocle | C4 | C23×C197 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C197 ◁ C2×C4×C197 ◁ G | |
60 conjugacy classes of subgroups.
2758 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #358×C197, #362×C197, C4×Q16×C197, … |
| maximal normal subgroup of | #358×C197, #362×C197, C4×Q16×C197, … |
| maximal quotient of | C2×#103×C197, C2×#107×C197, C4×Q16×C197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6304, 41);