Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C41 · Schur multiplier (H2) = C4 |
| direct product | C41×#2164 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C41 | C23 |
| commutator | C22 | C22×C8×C41 |
| Frattini, cosocle | C2×C8 | C23×C41 |
| socle | C22×C41 | C22×C8 |
| prime radical | C23×C41 | C2×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C41 ◁ G | |
138 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C41×#2164, C41×#33419, C41×#33420, … |
| maximal normal subgroup of | C2×C41×#2164, C41×#33419, C41×#33420, … |
| maximal quotient of | C41×#12592, C41×#12600, C41×#12654, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 896);