Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C29 ⋊ C2 |
| Sylow | C29 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C2×D29 |
| commutator, socle | C2×C29 | C22×C4 |
| Frattini | C4 | C22×D29 |
| Fitting | C2×C8×C29 | C2 |
| prime radical | #90805 | C2 |
| cosocle | C4×C29 | C23 |
| hypercenter | C2×C8 | D29 |
| hypocenter | C29 | #131 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C8 ◁ C2×C8 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^5,29|c^2=d,d^2=e,b^a=be,f^a=f^28244 conjugacy classes — view the full character table.
| maximal subgroup of | #14270946, #14270948, #14271278, … |
| maximal normal subgroup of | #14270946, #14270948, #14271278, … |
| maximal quotient of | #14271117, #14271118, #14271128, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 122);