Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C221 |
| direct product | C23×#2397 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C4 | C23 |
| commutator, Frattini, cosocle | C23 | C27 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
228053 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72233923, C23×#45355, #72261581, … |
| maximal normal subgroup of | C2×#72233923, C23×#45355, #72261581, … |
| maximal quotient of | C2×D4×#2397, C23×C4×#392, C22×#607767, … |
Past the SmallGroups library coverage — no SmallGroups id.