Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#6599 |
| Sylow | C29 ⋊ C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×#1181 |
| commutator | C2×C29 | C2×C8 |
| Fitting, prime radical | C23×C29 | C4 |
| socle | C22×C29 | C2×C4 |
| cosocle | C2×Dic29 | C22 |
| hypercenter | C23 | #1181 |
| hypocenter | C29 | C22⋊C8 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C23 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^5,29|a^2=c,c^2=e,b^a=bd,f^a=f^12,f^c=f^2876 conjugacy classes — view the full character table.
| maximal subgroup of | #14272006, #14272007, #14272008, … |
| maximal normal subgroup of | #14272006, #14272007, #14272008, … |
| maximal quotient of | #14272006, #14272008, D4⋊#6599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 87);