Finite Group DatabasebetaFinite Group Databasebeta| order | 9472 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C2 |
| direct product | C37×#12449 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | #459 |
| commutator, Frattini, cosocle | C4×C8 | C23×C37 |
| prime radical | C2×D8×C37 | D4 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C42×C37 ◁ C82×C37 ◁ G | |
222 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1591 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9472, 5437);