Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C23 ⋊ Q82 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D23 |
| commutator, socle, prime radical, cosocle | C22×C23 | C24 |
| Fitting | C23×C4⋊Q8 | C2 |
| hypercenter | C4⋊Q8 | D23 |
| hypocenter | C23 | Q82 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
212 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1472 |
Polycyclic presentation:
2^6,23|a^2=ef,b^2=e,c^2=f,d^2=e,b^a=be,c^a=cf,d^b=de,g^d=g^22179 conjugacy classes — view the full character table.
| maximal subgroup of | #15672473, #15672476, #15672535, … |
| maximal normal subgroup of | #15672473, #15672476, #15672535, … |
| maximal quotient of | #15676309, #15676311, #15676483, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1279);