Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1406 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C79 · Schur multiplier (H2) = C4 |
| direct product | C79×#1406 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | #353 |
| commutator | C42 | C2×C4×C79 |
| Frattini, cosocle | #124 | C22×C79 |
| prime radical | #496×C79 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C22×C79 ◁ C2×C4×C79 ◁ #124×C79 ◁ G | |
108 conjugacy classes of subgroups.
1106 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C79×#1406, C79×#13577, C79×#13578, … |
| maximal normal subgroup of | C2×C79×#1406, C79×#13577, C79×#13578, … |
| maximal quotient of | C79×#7352, C79×#7372, C79×#7402, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 138);