Finite Group DatabasebetaFinite Group Databasebeta| order | 37700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic9425 |
| derived, Hall | C13×C25×C29 ⋊ C4 |
| Hall | C25×C29 ⋊ Dic13 |
| Hall | C13×C29 ⋊ Dic25 |
| Hall | C13×C25 ⋊ Dic29 |
| Sylow | C29 ⋊ Dic325 |
| Sylow | C25 ⋊ Dic377 |
| Sylow | C13 ⋊ Dic725 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9425 |
| commutator, hypocenter | C13×C25×C29 | C4 |
| Frattini | C2×C5 | D1885 |
| Fitting, cosocle | C2×C13×C25×C29 | C2 |
| socle, prime radical | C2×C5×C13×C29 | D5 |
| LCS | G ▷ C13×C25×C29 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 37700 |
A minimal faithful permutation representation — 2 generators on 71 points:
(1,2)(3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(30,31,32,33,34,35,36,37,38,39,40,41,42)(43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71);(1,3,2,4)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)(44,71)(45,70)(46,69)(47,68)(48,67)(49,66)(50,65)(51,64)(52,63)(53,62)(54,61)(55,60)(56,59)(57,58)Polycyclic presentation:
2,5,13,29,2,5|a^2=e,b^5=f^4,b^a=b^4f,c^a=c^12,d^a=d^28,f^a=f^49428 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37700, 8);