Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊C4×C29 ⋊ C2 |
| Sylow | C29 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D29 |
| commutator | C2×C29 | C22×C4 |
| Fitting | C4⋊C4×C29 | C2 |
| socle, cosocle | C22×C29 | C23 |
| prime radical | C2×D116 | C2 |
| hypercenter | C4⋊C4 | D29 |
| hypocenter | C29 | C4×D4 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^5,29|b^2=e,c^2=d,b^a=be,f^a=f^28,c^b=ce160 conjugacy classes — view the full character table.
| maximal subgroup of | #14271243, #14271245, #14271248, … |
| maximal normal subgroup of | #14271243, #14271245, #14271248, … |
| maximal quotient of | #14271010, C4⋊C4×Dic29, #14271034, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 114);