Finite Group DatabasebetaFinite Group Databasebeta| order | 15584 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C487 ⋊ C2 |
| Sylow | C487 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D487 |
| commutator, socle, cosocle | C2×C487 | C24 |
| Fitting | #41×C487 | C2 |
| hypercenter | #41 | D487 |
| hypocenter | C487 | H(5,𝔽2) |
| LCS | G ▷ C2×C487 ▷ C487 | |
| UCS | C1 ◁ C2 ◁ #41 | |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3896 |
Polycyclic presentation:
2^5,487|b^a=be,d^a=de,c^b=ce,f^c=f^486,f^d=f^4862447 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44529216, #44529219, #44529226, … |
| maximal normal subgroup of | #44529216, #44529219, #44529226, … |
| maximal quotient of | #44529522, #44529524, #44529530, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15584, 192);