Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×D4×C571 ⋊ C2 |
| Sylow | C571 ⋊ #120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D571 |
| commutator, socle, cosocle | C22×C571 | C23 |
| Fitting | C2×D4×C571 | C2 |
| hypercenter | C2×D4 | D571 |
| hypocenter | C571 | #120 |
| LCS | G ▷ C22×C571 ▷ C571 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4568 |
Polycyclic presentation:
2^5,571|b^a=bd,c^a=ce,f^c=f^5702864 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49142052, #49142054, #49142453, … |
| maximal normal subgroup of | #49142052, #49142054, #49142453, … |
| maximal quotient of | #49142121, #49142137, #49142138, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 114);