Finite Group DatabasebetaFinite Group Databasebeta| order | 1552 |
| isoclinism | isoclinic class of D97 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C97 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D97 |
| commutator, hypocenter | C97 | C16 |
| Fitting, cosocle | C8×C97 | C2 |
| socle, prime radical | C2×C97 | C8 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C8 | |
10 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 1552 |
Polycyclic presentation:
2^4,97|a^2=b,b^2=c,c^2=d,e^a=e^96400 conjugacy classes — view the full character table.
| maximal subgroup of | C16×D97, C2×#13095486, #15690749, … |
| maximal normal subgroup of | C16×D97, C2×#13095486, #15690749, … |
| maximal quotient of | #15690716, C2×#13095486 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1552, 15);