Finite Group DatabasebetaFinite Group Databasebeta| order | 1400 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23×C5 |
| direct product | C22×C7×C5⋊D5 |
| Fitting, socle | C22×C52×C7 ⋊ C2 |
| derived, Sylow | C52 ⋊ C23×C7 |
| Hall | C52×C7 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C7 | C5⋊D5 |
| commutator, cosocle, hypocenter | C52 | C23×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C52×C7 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C7 | |
256 conjugacy classes of subgroups.
| transitive degree | μt(G) = 700 |
392 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C7×#1043, C22×D7×C5⋊D5, C22×C7⋊#1043, … |
| maximal normal subgroup of | C22×C7×#1043, C22×D7×C5⋊D5, C22×C7⋊#1043, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1400, 151);