Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C42×C29 ⋊ C2 |
| Sylow | C29 ⋊ #126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D29 |
| commutator, socle, cosocle | C22×C29 | C23 |
| Fitting | C42×C29 | C2 |
| prime radical | C22×D29 | C22 |
| hypercenter | C42 | D29 |
| hypocenter | C29 | #126 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C42 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^5,29|b^2=d,c^2=e,b^a=be,c^a=cde,f^a=f^28238 conjugacy classes — view the full character table.
| maximal subgroup of | #126×D29, C2×#11745238, #14271696, … |
| maximal normal subgroup of | #126×D29, C2×#11745238, #14271696, … |
| maximal quotient of | #14271031, #14271047, #14271054, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 97);