Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, Hall | C52×C112 ⋊ C2×D3 |
| derived, Hall | C52⋊(C112⋊C3) ⋊ C22 |
| Sylow | C112 ⋊ #3874⋊C2 |
| Sylow | C52 ⋊ C2×#10624391 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C52⋊(C112⋊C3) | C22 |
| Fitting, socle | C52×C112 | C2×D3 |
| LCS | G ▷ C52⋊(C112⋊C3) | |
| UCS | C1 | |
124 conjugacy classes of subgroups; only the 11 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 11 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 165 |
Polycyclic presentation:
2^2,3,5^2,11^2|c^a=c^2,d^a=d^4e^4,f^a=fg^4,g^a=g^10,d^b=d^4,e^b=e^4,d^c=e,e^c=d^4e^4,f^c=f^2g^10,g^c=f^7g^8384 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 711);