Finite Group DatabasebetaFinite Group Databasebeta| order | 992 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C31 ⋊ C2 |
| Sylow | C31 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×D31 |
| commutator, socle | C2×C31 | C2×C8 |
| Fitting | C16×C31 | C2 |
| prime radical | C2×D31 | C8 |
| cosocle | C8×C31 | C22 |
| hypercenter | C16 | D31 |
| hypocenter | C31 | M32 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C8 ◁ C16 | |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 496 |
Polycyclic presentation:
2^5,31|b^2=c,c^2=d,d^2=e,b^a=be,f^a=f^30260 conjugacy classes — view the full character table.
| maximal subgroup of | M32×D31, C2×#11758386, #14521465, … |
| maximal normal subgroup of | M32×D31, C2×#11758386, #14521465, … |
| maximal quotient of | #14520824, (C2×D31)⋊C16, Dic31⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(992, 4);