Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of C7⋊(C52⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | C22×C7⋊(C52⋊C3) |
| Fitting, socle, Hall | C22×C52×C7 ⋊ C3 |
| derived, Hall | C52×C7 ⋊ C22×C3 |
| Hall | C22×C52 ⋊ ΓL(1,𝔽8) |
| Hall | C22×C7 ⋊ C52⋊C3 |
| Sylow | C52 ⋊ C22×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C22×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C7⋊(C52⋊C3) |
| commutator, cosocle, hypocenter | C52×C7 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C52×C7 | C3 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C22 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 420 |
244 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 149);