Finite Group DatabasebetaFinite Group Databasebeta| order | 18818 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C97 |
| unambiguous semidirect product | C97⋊D97 |
| Fitting, socle, derived, Sylow | C972 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C972 | C2 |
| LCS | G ▷ C972 | |
| UCS | C1 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9409 |
Polycyclic presentation:
2,97^2|b^a=b^96,c^a=c^964706 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D972, #49178877, #49178878, … |
| maximal normal subgroup of | D972, #49178877, #49178878, … |
| maximal quotient of | #49178872, C2×C97⋊D97 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18818, 4);