Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C29 ⋊ C2 |
| Sylow | C29 ⋊ AGL(1,ℤ/8) |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D29 |
| commutator, cosocle | C4×C29 | C23 |
| Frattini | C4 | C22×D29 |
| Fitting | SD16×C29 | C2 |
| socle | C2×C29 | C2×D4 |
| hypercenter | SD16 | D29 |
| hypocenter | C29 | AGL(1,ℤ/8) |
| LCS | G ▷ C4×C29 ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ SD16 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 232 |
Polycyclic presentation:
2^5,29|c^2=e,d^2=e,c^a=ce,f^a=f^28,c^b=cd,d^b=de,d^c=de109 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/8)×D29, C2×#11745276, #14271960, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×D29, C2×#11745276, #14271960, … |
| maximal quotient of | #14271163, #14271166, #14271202, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 135);