Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4⋊C4×C571 ⋊ C2 |
| Sylow | C571 ⋊ #126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D571 |
| commutator, socle, cosocle | C22×C571 | C23 |
| Fitting | C4⋊C4×C571 | C2 |
| prime radical | C22×D571 | C22 |
| hypercenter | C4⋊C4 | D571 |
| hypocenter | C571 | #126 |
| LCS | G ▷ C22×C571 ▷ C571 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9136 |
Polycyclic presentation:
2^5,571|b^2=de,c^2=d,b^a=bd,c^a=ce,f^a=f^570,f^c=f^5702864 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #126×D571, C2×#32912689, #49142793, … |
| maximal normal subgroup of | #126×D571, C2×#32912689, #49142793, … |
| maximal quotient of | #49142133, #49142147, #49142149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 141);