Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #127×C181 ⋊ C2 |
| Sylow | C181 ⋊ #560 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D181 |
| commutator, socle, cosocle | C22×C181 | C24 |
| Fitting | #127×C181 | C2 |
| hypercenter | #127 | D181 |
| hypocenter | C181 | #560 |
| LCS | G ▷ C22×C181 ▷ C181 | |
| UCS | C1 ◁ C22 ◁ #127 | |
252 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,g^d=g^1801279 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37535727, #37535731, #560×D181, … |
| maximal normal subgroup of | #37535727, #37535731, #560×D181, … |
| maximal quotient of | #37536858, #37536871, #37536872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1286);