Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C23 ⋊ #446 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D23 |
| commutator, socle, prime radical | C22×C23 | C22×C4 |
| Fitting | C4×C8×C23 | C2 |
| cosocle | C2×C4×C23 | C23 |
| hypercenter | C4×C8 | D23 |
| hypocenter | C23 | #446 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C2×C4 ◁ C4×C8 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1472 |
Polycyclic presentation:
2^6,23|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^a=g^22380 conjugacy classes — view the full character table.
| maximal subgroup of | #15671378, #15671380, #15672233, … |
| maximal normal subgroup of | #15671378, #15671380, #15672233, … |
| maximal quotient of | #15673264, #15673271, #15673954, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 679);