Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C83 · Schur multiplier (H2) = C24×C42 |
| direct product | C83×#2309 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C83 | C24 |
| commutator | C22 | C23×C4×C83 |
| Frattini, cosocle | C23 | C24×C83 |
| prime radical | C23×D4×C83 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ G | |
1104 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 360 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
3652 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 1041);