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 | C23×#97 | C2 |
| cosocle | C2×C4×C23 | C23 |
| hypercenter | #97 | D23 |
| hypocenter | C23 | #446 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C2×C4 ◁ #97 | |
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^b=g^22248 conjugacy classes — view the full character table.
| maximal subgroup of | D23×#446, C2×#13092545, #15682328, … |
| maximal normal subgroup of | D23×#446, C2×#13092545, #15682328, … |
| maximal quotient of | #15673265, #15673269, #15673273, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 677);