Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q8×C181 ⋊ C2 |
| Sylow | C181 ⋊ #559 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D181 |
| commutator, socle, cosocle | C22×C181 | C24 |
| Fitting | C4×Q8×C181 | C2 |
| prime radical | #19153813 | C2 |
| hypercenter | C4×Q8 | D181 |
| hypocenter | C181 | #559 |
| LCS | G ▷ C22×C181 ▷ C181 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
236 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,181|a^2=f,b^2=ef,c^2=f,d^2=e,b^a=be,c^a=cf,d^b=de,g^b=g^1801825 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37532779, #37532782, #37532841, … |
| maximal normal subgroup of | #37532779, #37532782, #37532841, … |
| maximal quotient of | #37536676, #37536678, #37536690, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1284);