Finite Group DatabasebetaFinite Group Databasebeta| order | 3364 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Sylow | C841 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C841 | C4 |
| Frattini, socle | C29 | #1181 |
| prime radical, cosocle | D841 | C2 |
| LCS | G ▷ C841 | |
| UCS | C1 | |
9 conjugacy classes of subgroups.
| minimal degree | μ(G) = 841 |
| transitive degree | μt(G) = 841 |
Polycyclic presentation:
2^2,29^2|a^2=b,c^29=d,c^a=c^12d,d^a=d^12,c^b=c^28d^28,d^b=d^28214 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#16809850, #30681252, #30681253, … |
| maximal normal subgroup of | C5×#16809850, #16809850⋊C7, C7×#16809850, … |
| maximal quotient of | C5×#16809850, #30681252, #30681253, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3364, 4);