Finite Group DatabasebetaFinite Group Databasebeta| order | 5552 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C347 · Schur multiplier (H2) = C22 |
| direct product | C2×Q8×C347 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C347 | C22 |
| commutator, Frattini, cosocle | C2 | C23×C347 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C347 ◁ G | |
38 conjugacy classes of subgroups.
3470 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #101×C347, #103×C347, C4×Q8×C347, … |
| maximal normal subgroup of | #101×C347, #103×C347, C4×Q8×C347, … |
| maximal quotient of | C2×C4⋊C4×C347, C4×Q8×C347, C22⋊Q8×C347, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5552, 12);