Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C29 ⋊ C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D29 |
| commutator, socle, prime radical, cosocle | C22×C29 | C23 |
| Fitting | C2×Q8×C29 | C2 |
| hypercenter | C2×Q8 | D29 |
| hypocenter | C29 | C4⋊Q8 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^5,29|a^2=e,b^2=d,c^2=d,c^a=ce,f^a=f^28,c^b=cd154 conjugacy classes — view the full character table.
| maximal subgroup of | #14270961, #14271344, #14271346, … |
| maximal normal subgroup of | #14270961, #14271344, #14271346, … |
| maximal quotient of | #14271032, #14271058, #14271068, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 165);