Finite Group DatabasebetaFinite Group Databasebeta| order | 944 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C59 ⋊ C2 |
| Sylow | C59 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D59 |
| commutator, socle, cosocle | C2×C59 | C23 |
| Fitting | Q8×C59 | C2 |
| hypercenter | Q8 | D59 |
| hypocenter | C59 | #41 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 472 |
Polycyclic presentation:
2^4,59|b^2=d,c^2=d,c^a=cd,e^a=e^58,c^b=cd155 conjugacy classes — view the full character table.
| maximal subgroup of | #14273748, #14273750, #14273754, … |
| maximal normal subgroup of | #14273748, #14273750, #14273754, … |
| maximal quotient of | #14273685, #14273689, Q8×Dic59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(944, 34);