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C2×C7×#2370 #13211360

order1792
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C4×C7 · Schur multiplier (H2) = C28

Aliases

direct productC2×C7×#2370

Subgroups

subgroupG/H
center, socle, prime radicalC24×C7C24
commutatorC22C24×C4×C7
Frattini, cosocleC23C25×C7
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

2510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 1792

A minimal faithful permutation representation — 5 generators on 29 points:

(1,2)(23,24,25,26,27,28,29);(3,4,6,5)(7,8,11,10)(9,13,14,12)(15,16)(17,21)(18,22)(19,20);(3,5,6,4)(8,10)(12,13)(16,20)(18,21);(7,9)(8,12)(10,13)(11,14)(15,17,19,22)(16,21,20,18);(7,10,11,8)(9,13,14,12)(15,18,19,21)(16,22,20,17)

Conjugacy classes & character table

700 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 27132);