Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C79 · Schur multiplier (H2) = C23 |
| direct product | C79×#1280 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C79 | C22⋊C4 |
| commutator | C22 | C4×C8×C79 |
| Frattini, cosocle | C23×C4 | C22×C79 |
| prime radical | C24×C79 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C79 ◁ C23×C4×C79 ◁ G | |
264 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
3476 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C79×#7103, C79×#7104, C79×#7122, … |
| maximal normal subgroup of | C79×#7103, C79×#7104, C79×#7122, … |
| maximal quotient of | C79×#7016, C79×#7017, C79×#7020, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 12);