Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#1181)⋊C4 |
| Fitting | C2×C4×C29 ⋊ C4 |
| Sylow | C29 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×#1181 |
| commutator | C2×C29 | C42 |
| Fitting | C2×C4×C29 | C4 |
| socle | C22×C29 | C2×C4 |
| prime radical, cosocle | C22×D29 | C22 |
| hypercenter | C2×C4 | #1181 |
| hypocenter | C29 | #95 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 232 |
Polycyclic presentation:
2^5,29|a^2=c,b^2=d,b^a=be,f^a=f^12,f^c=f^2876 conjugacy classes — view the full character table.
| maximal subgroup of | #14272014, #14272015, #14272016, … |
| maximal normal subgroup of | #14272014, #14272015, #14272016, … |
| maximal quotient of | (C2×#1181)⋊C8, #14272029, #14272030, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 81);