Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C173 · Schur multiplier (H2) = C26×C42 |
| direct product | C2×H(3,𝔽4)×C173 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C173 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C173 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C173 ◁ G | |
1408 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5536 |
6574 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 2258);