Finite Group DatabasebetaFinite Group Databasebeta| order | 1352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C132 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D132 |
| commutator, Fitting, socle, cosocle | C2×C132 | C22 |
| hypocenter | C132 | D4 |
| LCS | G ▷ C2×C132 ▷ C132 | |
| UCS | C1 ◁ C2 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 104 |
Polycyclic presentation:
2^3,13^2|b^a=bc,e^a=e^12,d^b=d^12125 conjugacy classes — view the full character table.
| maximal subgroup of | #72229261, #72229264, #72259216, … |
| maximal normal subgroup of | #72229261, #72229264, #72259216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1352, 24);