Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C157 · Schur multiplier (H2) = C23 |
| direct product | #449×C157 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C157 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C157 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C157 ◁ C22×C4×C157 ◁ G | |
162 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2983 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#449×C157, #3002×C157, #3005×C157, … |
| maximal normal subgroup of | C2×#449×C157, #3002×C157, #3005×C157, … |
| maximal quotient of | #1597×C157, #1600×C157, #1609×C157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 130);