Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C79 · Schur multiplier (H2) = C2 |
| direct product | C79×#1330 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C79 | C22⋊C4 |
| commutator | C2×C4 | C2×C8×C79 |
| Frattini, cosocle | C4×C8 | C22×C79 |
| socle | C22×C79 | C22⋊C8 |
| prime radical | C2×D4×C79 | C8 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C79 ◁ C4×C8×C79 ◁ G | |
100 conjugacy classes of subgroups.
3002 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C79×#1330, C79×#11586, C79×#11587, … |
| maximal normal subgroup of | C2×C79×#1330, C79×#11586, C79×#11587, … |
| maximal quotient of | C79×#7072, C79×#7073, C79×#7074, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 62);