Finite Group DatabasebetaFinite Group Databasebeta| order | 1352 |
| isoclinism | isoclinic class of #10621721 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C169 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10621721 |
| commutator, hypocenter | C169 | C8 |
| Frattini, socle, prime radical | C2×C13 | #261 |
| Fitting | C2×C169 | C4 |
| cosocle | Dic169 | C2 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 177 |
| transitive degree | μt(G) = 1352 |
Polycyclic presentation:
2^3,13^2|a^2=b,b^2=c,d^13=e,d^a=d^8e^7,e^a=e^8,d^b=d^12e^12,e^b=e^1292 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1352, 3);