Finite Group DatabasebetaFinite Group Databasebeta| order | 2528 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C79 ⋊ C2 |
| Sylow | C79 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×D79 |
| commutator, socle | C2×C79 | C2×C8 |
| Fitting | C16×C79 | C2 |
| prime radical | C2×D79 | C8 |
| cosocle | C8×C79 | C22 |
| hypercenter | C16 | D79 |
| hypocenter | C79 | M32 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C8 ◁ C16 | |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 1264 |
Polycyclic presentation:
2^5,79|a^2=c,c^2=d,d^2=e,b^a=be,f^b=f^78644 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2528, 85);