Finite Group DatabasebetaFinite Group Databasebeta| order | 27008 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C211 · Schur multiplier (H2) = C24 |
| direct product | #2724×C211 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C211 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C211 |
| prime radical | C22×D4×C211 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C211 ◁ G | |
504 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 13504 |
6752 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27008, 1456);