Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #3415 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C83 · Schur multiplier (H2) = C25 |
| direct product | C83×#3415 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C83 | C22×D8 |
| commutator, Frattini, cosocle | C8 | C24×C83 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C83 ◁ #41×C83 ◁ #131×C83 ◁ G | |
370 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2656 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2147);