Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C157 · Schur multiplier (H2) = C25 |
| direct product | #525×C157 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C157 | C23 |
| commutator, Frattini, cosocle | C22 | C24×C157 |
| socle | C22×C157 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C157 ◁ G | |
330 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
4396 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1501×C157, #1504×C157, #1513×C157, … |
| maximal normal subgroup of | #1501×C157, #1504×C157, #1513×C157, … |
| maximal quotient of | #2280×C157, #2290×C157, #2296×C157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 206);