Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C79 · Schur multiplier (H2) = C22 |
| direct product | C79×#1295 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C79 | C22⋊C4 |
| commutator | C2×C4 | C42×C79 |
| Frattini, cosocle | C2×C42 | C22×C79 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C79 ◁ C2×C42×C79 ◁ G | |
180 conjugacy classes of subgroups.
3002 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C79×#7416, C79×#7442, C2×C79×#1295, … |
| maximal normal subgroup of | C79×#7416, C79×#7442, C2×C79×#1295, … |
| maximal quotient of | C79×#7025, C79×#7030, C79×#7036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 27);