Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12366 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C41 · Schur multiplier (H2) = C22 |
| direct product | C41×#12366 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C41 | #1629 |
| commutator, Frattini, cosocle | C4×C8 | C23×C41 |
| prime radical | C41×#3292 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C2×C4×C41 ◁ C4×C8×C41 ◁ G | |
364 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1148 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 5354);