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C5×C11×2−1+4 #13183460

order1760
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C24×C5×C11 · Schur multiplier (H2) = C25

Aliases

direct productC5×C11×2−1+4

Subgroups

subgroupG/H
center, socleC2×C5×C11C24
commutator, Frattini, cosocleC2C24×C5×C11
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C5×C11 ◁ G

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 880

A minimal faithful permutation representation — 4 generators on 32 points:

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

Conjugacy classes & character table

935 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1269);