Finite Group DatabasebetaFinite Group Databasebeta| order | 25652 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
No aliases for this group.
| Fitting, socle, derived, Hall | C112×C53 ⋊ C4 |
| Sylow | C112 ⋊ #6157 |
| Sylow | C53 ⋊ #92150 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C112×C53 | C4 |
| prime radical, cosocle | C11⋊D583 | C2 |
| LCS | G ▷ C112×C53 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1166 |
Polycyclic presentation:
2^2,11^2,53|a^2=b,c^a=c^8d^8,d^a=c^7d^3,e^a=e^30,c^b=c^10,d^b=d^10,e^b=e^521607 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25652, 20);