Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C23×2−1+4 ⋊ C2 |
| Sylow | C23 ⋊ #578 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×C22⋊D23 |
| commutator, cosocle | C4×C23 | C24 |
| Frattini | C4 | C23×D23 |
| Fitting | C23×2−1+4 | C2 |
| socle | C2×C23 | C22×D4 |
| hypercenter | 2−1+4 | D23 |
| hypocenter | C23 | #578 |
| LCS | G ▷ C4×C23 ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ 2−1+4 | |
248 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 107 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|a^2=f,b^2=f,e^2=f,b^a=be,e^a=ef,e^b=ef,g^b=g^22,d^c=df209 conjugacy classes — view the full character table.
| maximal subgroup of | #15685167, #15685168, #15685170, … |
| maximal normal subgroup of | #15685167, #15685168, #15685170, … |
| maximal quotient of | #15681927, #15681930, #15681995, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1364);