Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C22×#41×C23 ⋊ C2 |
| Sylow | C23 ⋊ #3449 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D23 |
| commutator, socle, cosocle | C22×C23 | C25 |
| Frattini | C22 | C24×D23 |
| Fitting | C22×#41×C23 | C2 |
| hypercenter | C22×#41 | D23 |
| hypocenter | C23 | #3449 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C2×C4 ◁ C22×#41 | |
1556 conjugacy classes of subgroups.
| transitive degree | μt(G) = 736 |
Polycyclic presentation:
2^7,23|e^2=f,b^a=bf,c^a=cg,d^a=df,c^b=cf,h^c=h^22484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 17839);