Finite Group DatabasebetaFinite Group Databasebeta| order | 4096 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C29 · Schur multiplier (H2) = C234 |
| direct product | C23×#7667013 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C4 | C25 |
| commutator, Frattini, cosocle | C23 | C29 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
14002171 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1024 |
1024 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×#72236189 |
| maximal normal subgroup of | C23×#72236189 |
Past the SmallGroups library coverage — no SmallGroups id.