Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #353 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C47 · Schur multiplier (H2) = C23 |
| direct product | C2×C47×#355 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C47 | #99 |
| commutator | C2×C4 | C22×C4×C47 |
| Frattini, cosocle | C2×Q8 | C23×C47 |
| prime radical | C22×D4×C47 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C23×C47 ◁ C22×Q8×C47 ◁ G | |
260 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1222 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×#7487, C47×#7495, C47×#7502, … |
| maximal normal subgroup of | C47×#7487, C47×#7495, C47×#7502, … |
| maximal quotient of | C2×C47×#1318, C2×C47×#1324, C47×#11476, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 862);