Finite Group DatabasebetaFinite Group Databasebeta| order | 27392 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C107 · Schur multiplier (H2) = C210 |
| direct product | C2×C107×#2380 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C107 | C24 |
| commutator | C22 | C24×C4×C107 |
| Frattini, cosocle | C23 | C25×C107 |
| prime radical | C22×#127×C107 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C107 ◁ G | |
3798 conjugacy classes of subgroups; only the 1486 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 1486 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 13696 |
8132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27392, 27332);