Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C23 ⋊ #1445 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D23 |
| commutator | C23×C23 | C22×C4 |
| Fitting | C2×C23×#95 | C2 |
| socle, prime radical, cosocle | C24×C23 | C23 |
| hypercenter | C2×#95 | D23 |
| hypocenter | C23 | #1445 |
| LCS | G ▷ C23×C23 ▷ C23 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
520 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 193 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2944 |
Polycyclic presentation:
2^7,23|a^2=g,b^2=de,c^2=de,b^a=bd,c^a=ce,c^b=cf,h^b=h^22,h^c=h^22484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 2777);