Finite Group DatabasebetaFinite Group Databasebeta| order | 3524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C881 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C881 | C4 |
| prime radical, cosocle | D881 | C2 |
| LCS | G ▷ C881 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 881 |
| transitive degree | μt(G) = 881 |
Polycyclic presentation:
2^2,881|a^2=b,c^a=c^387,c^b=c^880224 conjugacy classes — view the full character table.
| maximal subgroup of | #16812931⋊C5, C5×#16812931, #31798613, … |
| maximal normal subgroup of | #16812931⋊C5, C5×#16812931, C7×#16812931 |
| maximal quotient of | C5×#16812931, #31798613, #31798614, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3524, 3);