Finite Group DatabasebetaFinite Group Databasebeta| order | 15968 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C499 ⋊ C2 |
| Sylow | C499 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D499 |
| commutator, socle, cosocle | C2×C499 | C24 |
| Fitting | #41×C499 | C2 |
| hypercenter | #41 | D499 |
| hypocenter | C499 | H(5,𝔽2) |
| LCS | G ▷ C2×C499 ▷ C499 | |
| UCS | C1 ◁ C2 ◁ #41 | |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3992 |
Polycyclic presentation:
2^5,499|b^a=be,d^a=de,c^b=ce,f^c=f^498,f^d=f^4982507 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44543264, #44543267, #44543274, … |
| maximal normal subgroup of | #44543264, #44543267, #44543274, … |
| maximal quotient of | #44543570, #44543572, #44543578, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15968, 192);