Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C83 · Schur multiplier (H2) = C22 |
| direct product | C83×#1317 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | #99 |
| commutator | C23 | C2×C8×C83 |
| Frattini, cosocle | C2×C22⋊C4 | C22×C83 |
| prime radical | C24×C83 | C2×C4 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C23×C83 ◁ C2×C22⋊C4×C83 ◁ G | |
150 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2158 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 49);