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C2×C7×#2507 #13211986

order1792
nilpotency class2
isoclinismisoclinic class of #2403
automorphism?
homologyAbelianization (H1) = C25×C7 · Schur multiplier (H2) = C27

Aliases

direct productC2×C7×#2507

Subgroups

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

2054 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 1792

A minimal faithful permutation representation — 5 generators on 33 points:

(1,2)(27,28,29,30,31,32,33);(3,4)(5,9)(6,7)(8,10)(12,14)(13,17)(19,20,22,24)(21,25,26,23);(4,7)(8,9)(11,12,15,14)(13,18,17,16)(19,20)(21,23)(22,24)(25,26);(3,4)(5,8)(6,7)(9,10)(11,13,15,17)(12,16,14,18);(3,5,6,10)(4,8,7,9)(11,14,15,12)(13,18,17,16)(19,21,22,26)(20,23,24,25)

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, 27758);