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C17×#10405 #16868149

order4352
nilpotency class3
isoclinismisoclinic class of #9914
automorphism?
homologyAbelianization (H1) = C23×C17 · Schur multiplier (H2) = C23

Aliases

direct productC17×#10405

Subgroups

subgroupG/H
center, socleC23×C17#120
commutator, Frattini, cosocleC23×C4C23×C17
prime radicalC2×C17×#121C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C17 ◁ C23×C4×C17 ◁ G

646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 1088

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,20)(22,23,25,24)(26,28,27,29)(30,31)(32,34)(33,35)(36,37);(18,19)(20,21)(22,24)(23,25)(26,28)(27,29)(30,32)(31,34)(33,36)(35,37);(18,20,21,19)(23,28)(24,29)(26,27)(34,37)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3393);