Finite Group DatabasebetaFinite Group Databasebeta| order | 2164 |
| isoclinism | isoclinic class of #14524194 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C541 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C541 | C4 |
| prime radical, cosocle | D541 | C2 |
| LCS | G ▷ C541 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 541 |
| transitive degree | μt(G) = 541 |
Polycyclic presentation:
2^2,541|a^2=b,c^a=c^52,c^b=c^540139 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14524194, #14524194⋊C5, C5×#14524194, … |
| maximal normal subgroup of | C2×#14524194, #14524194⋊C5, C5×#14524194, … |
| maximal quotient of | #16864520, C2×#14524194, C5×#14524194, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2164, 3);