Finite Group DatabasebetaFinite Group Databasebeta| order | 2163 |
| isoclinism | isoclinic class of #14524189 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C103 ⋊ C3 |
| Sylow | C103 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C103⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C103 | C3 |
| LCS | G ▷ C7×C103 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 110 |
| transitive degree | μt(G) = 721 |
Polycyclic presentation:
3,7,103|b^a=b^2,c^a=c^46243 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14524189, #16864498, #16864502, … |
| maximal normal subgroup of | C2×#14524189, #16864498, #16864502, … |
| maximal quotient of | C2×#14524189, C5×#14524189, #29502871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2163, 3);