Finite Group DatabasebetaFinite Group Databasebeta| order | 16004 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C4001 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C4001 | C4 |
| prime radical, cosocle | D4001 | C2 |
| LCS | G ▷ C4001 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4001 |
Polycyclic presentation:
2^2,4001|a^2=b,c^a=c^3102,c^b=c^40001004 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#30630749, #44544949 |
| maximal normal subgroup of | C2×#30630749, #44544949 |
| maximal quotient of | #44544947, C2×#30630749 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16004, 3);