Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C23 ⋊ #322 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C2×D23 |
| commutator | C2×C23 | C4×C8 |
| Fitting | C4×C8×C23 | C2 |
| socle, prime radical | C22×C23 | C42 |
| cosocle | C42×C23 | C22 |
| hypercenter | C4×C8 | D23 |
| hypocenter | C23 | #322 |
| LCS | G ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1472 |
Polycyclic presentation:
2^6,23|a^2=c,b^2=d,c^2=e,d^2=f,b^a=be,g^b=g^22392 conjugacy classes — view the full character table.
| maximal subgroup of | #15671317, #15671319, #15671372, … |
| maximal normal subgroup of | #15671317, #15671319, #15671372, … |
| maximal quotient of | C23⋊#1273, #15671315, #15671317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 270);