Finite Group DatabasebetaFinite Group Databasebeta| order | 884 |
| isoclinism | isoclinic class of #11725131 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C17 ⋊ C4 |
| Sylow | C17 ⋊ #261 |
| Sylow | C13 ⋊ #595 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C17 | C4 |
| prime radical, cosocle | D221 | C2 |
| LCS | G ▷ C13×C17 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 221 |
Polycyclic presentation:
2^2,13,17|a^2=b,c^a=c^8,d^a=d^13,c^b=c^12,d^b=d^1659 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊#595, C2×#11725131, #11725131⋊C3, … |
| maximal normal subgroup of | D13⋊#595, C2×#11725131, #11725131⋊C3, … |
| maximal quotient of | #13183724, C2×#11725131, C3×#11725131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(884, 8);