Finite Group DatabasebetaFinite Group Databasebeta| order | 33756 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic8439 |
| unambiguous semidirect product | C3⋊Dic2813 |
| derived, Hall | C3×C29×C97 ⋊ C4 |
| Hall | C29×C97 ⋊ Dic3 |
| Hall | C3×C97 ⋊ Dic29 |
| Sylow | C97 ⋊ Dic87 |
| Hall | C3×C29 ⋊ Dic97 |
| Sylow | C29 ⋊ Dic291 |
| Sylow | C3 ⋊ Dic2813 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D8439 |
| commutator, hypocenter | C3×C29×C97 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C29×C97 | C2 |
| LCS | G ▷ C3×C29×C97 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 33756 |
A minimal faithful permutation representation — 2 generators on 133 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)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133);(1,3,2,4)(6,7)(9,36)(10,35)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(38,133)(39,132)(40,131)(41,130)(42,129)(43,128)(44,127)(45,126)(46,125)(47,124)(48,123)(49,122)(50,121)(51,120)(52,119)(53,118)(54,117)(55,116)(56,115)(57,114)(58,113)(59,112)(60,111)(61,110)(62,109)(63,108)(64,107)(65,106)(66,105)(67,104)(68,103)(69,102)(70,101)(71,100)(72,99)(73,98)(74,97)(75,96)(76,95)(77,94)(78,93)(79,92)(80,91)(81,90)(82,89)(83,88)(84,87)(85,86)Polycyclic presentation:
2,3,29,97,2|a^2=e,b^a=b^2,c^a=c^28,d^a=d^968442 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33756, 9);