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C2×C7×#2506 #13211977

order1792
nilpotency class2
isoclinismisoclinic class of #2403
automorphism?
homologyAbelianization (H1) = C25×C7 · Schur multiplier (H2) = C28

Aliases

direct productC2×C7×#2506

Subgroups

subgroupG/H
center, socle, prime radicalC24×C7C24
commutator, Frattini, cosocleC23C25×C7
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

2358 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);(4,5)(8,11)(9,13)(15,16,19,17)(18,21,22,20);(3,4,6,5)(7,8)(9,12)(10,11)(13,14)(15,17,19,16)(18,20,22,21);(3,4,6,5)(15,18,19,22)(16,20,17,21);(3,5,6,4)(7,9,10,13)(8,12,11,14)

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 27749);