Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C29 ⋊ C2 |
| Sylow | C29 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D29 |
| commutator, socle, cosocle | C2×C29 | C24 |
| Fitting | #41×C29 | C2 |
| hypercenter | #41 | D29 |
| hypocenter | C29 | H(5,𝔽2) |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C2 ◁ #41 | |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 232 |
Polycyclic presentation:
2^5,29|d^2=e,d^a=de,f^a=f^28,c^b=ce157 conjugacy classes — view the full character table.
| maximal subgroup of | #14271329, #14271332, #14271339, … |
| maximal normal subgroup of | #14271329, #14271332, #14271339, … |
| maximal quotient of | #14271635, #14271637, #14271643, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 223);