Finite Group DatabasebetaFinite Group Databasebeta| order | 11025 |
| isoclinism | isoclinic class of C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C72×C9 · Schur multiplier (H2) = C5×C7 |
| direct product | C72×C52⋊C9 |
| unambiguous semidirect product | C52⋊(C72×C9) |
| derived, Sylow | C52 ⋊ C72×C9 |
| Hall | C52×C72 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C72 | C52⋊C3 |
| commutator, hypocenter | C52 | C72×C9 |
| Frattini | C3 | C72×C52⋊C3 |
| Fitting, socle, prime radical | C3×C52×C72 | C3 |
| cosocle | C3×C52 | C3×C72 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C72 | |
100 conjugacy classes of subgroups.
1617 conjugacy classes. The character table is too large to display.
| derived subgroup of | C7⋊(C7⋊#90646) |
| maximal subgroup of | C72×#90646, C7×C7⋊#90646, C7⋊(C7⋊#90646), … |
| maximal normal subgroup of | C72×#90646, C7×C7⋊#90646, C7⋊(C7⋊#90646), … |
| maximal quotient of | C2×C72×C52⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11025, 27);