Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C210 · Schur multiplier (H2) = C244 |
| direct product | C23×#63103 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C4 | C26 |
| commutator, Frattini, cosocle | C2 | C210 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C2 ▷ C1 | |
230113640 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
1040 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×H(9,𝔽2), C22×#72258201, C23×2−1+8 |
| maximal normal subgroup of | C23×H(9,𝔽2), C22×#72258201, C23×2−1+8 |
Past the SmallGroups library coverage — no SmallGroups id.