Finite Group DatabasebetaFinite Group Databasebeta| order | 30282 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C103 ⋊ C2×C3 |
| Hall | C7×#14524190 ⋊ C2 |
| Hall | C7⋊D721 ⋊ C3 |
| Sylow | C103 ⋊ ΓL(1,𝔽8)⋊D7 |
| Sylow | C72 ⋊ D103⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C103 | C2×C3 |
| LCS | G ▷ C72×C103 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 2163 |
A minimal faithful permutation representation — 2 generators on 117 points:
(2,5,6,3,4,7)(9,10)(11,12)(13,14)(16,20,21,17,18,22)(19,28,29,23,24,38)(25,41,42,31,32,55)(26,40,36,34,30,27)(33,60,61,44,45,78)(35,58,59,47,43,52)(37,39,57,49,50,53)(46,83,84,63,64,102)(48,81,82,66,62,75)(51,56,80,68,69,76)(54,93,91,72,73,71)(65,94,95,74,86,110)(67,105,106,87,85,99)(70,79,104,88,89,100)(77,112,108,96,97,92)(90,103,111,98,107,116)(101,117,115,113,114,109);(1,2,4,7,6,5,3)(8,9,11,13,14,12,10)(15,16,19,25,33,46,65,72,50,24,30,38,52,71,92,109,113,89,45,62,73,76,78,99,84,104,112,86,105,83,103,114,116,110,82,42,57,58,41,56,77,98,88,68,49,36,21,20,26,35,48,67,87,66,47,34,18,22,27,37,51,70,90,96,69,32,43,53,55,75,95,111,117,107,64,85,94,97,100,102,106,61,80,93,81,60,79,101,115,108,91,59,29,40,28,39,54,74,63,44,31,23,17)Polycyclic presentation:
2,3,7^2,103|c^a=c^6,d^a=d^6,e^a=e^102,c^b=c^2,e^b=e^56855 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30282, 40);