Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C23 ⋊ #2321 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D23 |
| commutator | C22×C23 | C23×C4 |
| Fitting, prime radical | C2×C23×#120 | C2 |
| socle, cosocle | C23×C23 | C24 |
| hypercenter | C2×#120 | D23 |
| hypocenter | C23 | #2321 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
808 conjugacy classes of subgroups.
| transitive degree | μt(G) = 736 |
Polycyclic presentation:
2^7,23|a^2=g,b^2=g,b^a=be,c^a=cf,d^a=de,h^a=h^22,c^b=ce,h^b=h^22352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 7171);