Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C213 |
| direct product | C2×#72210587 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #23900 |
| commutator, Frattini, cosocle | C23×D4 | C25 |
| LCS | G ▷ C23×D4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C25 ◁ C23×#120 ◁ G | |
| LECS | G ▷ C23×D4 ▷ C23 ▷ C2 ▷ C1 | |
At least 6551 conjugacy classes of subgroups; only the 832 normal subgroups are shown.
152 conjugacy classes — view the full character table.
| maximal subgroup of | #72260825, C2×#72215688, C2×#72216913, … |
| maximal normal subgroup of | #72260825, C2×#72215688, C2×#72216398, … |
| maximal quotient of | C2×#72216737, #72338930 |
Past the SmallGroups library coverage — no SmallGroups id.