Finite Group DatabasebetaFinite Group Databasebeta| order | 11025 |
| isoclinism | isoclinic class of #3861 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C9 · Schur multiplier (H2) = C5 |
| direct product | C52×#89204 |
| derived, Sylow | C72 ⋊ C52×C9 |
| Hall | C52×C72 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C52 | #3861 |
| commutator, hypocenter | C72 | C52×C9 |
| Frattini | C3 | C52×#3861 |
| Fitting, socle, prime radical | C3×C52×C72 | C3 |
| cosocle | C3×C72 | C3×C52 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C52 | |
240 conjugacy classes of subgroups.
1425 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×#11725077, C52×#11725076, C5×C5⋊#11725077, … |
| maximal normal subgroup of | C52×#11725077, C52×#11725076, C5×C5⋊#11725077, … |
| maximal quotient of | C2×C52×#89204 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11025, 25);