Finite Group DatabasebetaFinite Group Databasebeta| order | 2528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C79 ⋊ C2 |
| Sylow | C79 ⋊ AGL(1,ℤ/8) |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D316 |
| commutator, cosocle | C4×C79 | C23 |
| Frattini | C4 | C22×D79 |
| Fitting | M16×C79 | C2 |
| socle | C2×C79 | C2×D4 |
| hypercenter | M16 | D79 |
| hypocenter | C79 | AGL(1,ℤ/8) |
| LCS | G ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ M16 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 632 |
Polycyclic presentation:
2^5,79|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^78,d^b=de,f^b=f^78401 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2528, 174);