Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C71 · Schur multiplier (H2) = C29 |
| direct product | C71×#14336 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C71 | C24 |
| commutator | C23 | C23×C4×C71 |
| Frattini, cosocle | C24 | C24×C71 |
| prime radical | C25×C71 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C71 ◁ G | |
3998 conjugacy classes of subgroups; only the 702 normal subgroups are shown.
This group has 3998 conjugacy classes of subgroups — too many to draw. Only its 702 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9088 |
4544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 7324);