Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×#1373 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C79 | D8 |
| commutator | C8 | C2×C8×C79 |
| Frattini, cosocle | C4×C8 | C22×C79 |
| socle | C2×C79 | #335 |
| prime radical | C22×C79 | #108 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C79 ◁ C2×C8×C79 ◁ C4×C8×C79 ◁ G | |
62 conjugacy classes of subgroups.
3476 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C79×#7387, C79×#7388, C79×#7447, … |
| maximal normal subgroup of | C79×#7387, C79×#7388, C79×#7447, … |
| maximal quotient of | C79×#7100, C79×#7101, C79×#7160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 105);