Finite Group DatabasebetaFinite Group Databasebeta| order | 37378 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D18689 |
| unambiguous semidirect product | C11⋊D1699 |
| unambiguous semidirect product | C1699⋊D11 |
| Fitting, socle, derived, Hall | C11×C1699 ⋊ C2 |
| Sylow | C1699 ⋊ D11 |
| Sylow | C11 ⋊ D1699 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C1699 | C2 |
| LCS | G ▷ C11×C1699 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1710 |
| transitive degree | μt(G) = 18689 |
A minimal faithful permutation representation — 2 generators on 1710 points:
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(780,943)(781,942)(782,941)(783,940)(784,939)(785,938)(786,937)(787,936)(788,935)(789,934)(790,933)(791,932)(792,931)(793,930)(794,929)(795,928)(796,927)(797,926)(798,925)(799,924)(800,923)(801,922)(802,921)(803,920)(804,919)(805,918)(806,917)(807,916)(808,915)(809,914)(810,913)(811,912)(812,911)(813,910)(814,909)(815,908)(816,907)(817,906)(818,905)(819,904)(820,903)(821,902)(822,901)(823,900)(824,899)(825,898)(826,897)(827,896)(828,895)(829,894)(830,893)(831,892)(832,891)(833,890)(834,889)(835,888)(836,887)(837,886)(838,885)(839,884)(840,883)(841,882)(842,881)(843,880)(844,879)(845,878)(846,877)(847,876)(848,875)(849,874)(850,873)(851,872)(852,871)(853,870)(854,869)(855,868)(856,867)(857,866)(858,865)(859,864)(860,863)(861,862)Polycyclic presentation:
2,11,1699|b^a=b^10,c^a=c^16989346 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37378, 3);