Finite Group DatabasebetaFinite Group Databasebeta| order | 992 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×D4×C31 ⋊ C2 |
| Sylow | C31 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D31 |
| commutator, socle, cosocle | C2×C31 | C24 |
| Fitting | C2×D4×C31 | C2 |
| hypercenter | C2×D4 | D31 |
| hypocenter | C31 | H(5,𝔽2) |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 248 |
Polycyclic presentation:
2^5,31|d^a=de,f^a=f^30,c^b=ce167 conjugacy classes — view the full character table.
| maximal subgroup of | #14521216, #14521219, #14521226, … |
| maximal normal subgroup of | #14521216, #14521219, #14521226, … |
| maximal quotient of | #14521521, #14521522, #14521524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(992, 179);