Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×Q8×C23 ⋊ C2 |
| Sylow | C23 ⋊ #536 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D23 |
| commutator, socle, cosocle | C22×C23 | C24 |
| Fitting | C22×Q8×C23 | C2 |
| prime radical | C2×#67288 | C2 |
| hypercenter | C22×Q8 | D23 |
| hypocenter | C23 | #536 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
270 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 736 |
Polycyclic presentation:
2^6,23|b^2=e,c^2=e,b^a=be,c^a=cf,d^a=de,g^a=g^22,c^b=ce242 conjugacy classes — view the full character table.
| maximal subgroup of | #15673916, #15673932, #15673934, … |
| maximal normal subgroup of | #15673916, #15673932, #15673934, … |
| maximal quotient of | #15675983, #15675990, #15676021, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1123);