Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of #14523608 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C52×C7 ⋊ C3×C4 |
| Hall | C7⋊#1043 ⋊ C3 |
| Hall | C7⋊(C52⋊C3) ⋊ C4 |
| Sylow | C52 ⋊ ΓL(1,𝔽8)⋊C4 |
| Sylow | C7 ⋊ #1043⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C7 | C3×C4 |
| prime radical | (C5⋊D5)⋊ΓL(1,𝔽8) | C2 |
| cosocle | C7×C5⋊D5 | C2×C3 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 105 |
Polycyclic presentation:
2,3,2,5^2,7|a^2=c,d^a=d^3,e^a=e^3,f^a=f^6,d^b=de,e^b=d^2e^3,f^b=f^4,d^c=d^4,e^c=e^428 conjugacy classes — view the full character table.
| maximal subgroup of | #28412943, C7×#14523608, #28413357, … |
| maximal normal subgroup of | C7×#14523608, C11×#14523608, C13×#14523608, … |
| maximal quotient of | #28412943, C7×#14523608, #28413357, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 88);