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C17×#34328 #16892072

order4352
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28

Aliases

direct productC17×#34328

Subgroups

subgroupG/H
center, socle, prime radicalC23×C17C25
commutatorC22C24×C4×C17
Frattini, cosocleC23C25×C17
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C17 ◁ G

2036 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 4352

A minimal faithful permutation representation — 5 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(22,23,26,25)(24,28,29,27)(31,32)(34,42)(36,38)(40,45);(30,31,35,32)(33,38,41,36)(34,37,42,39)(40,44,45,43);(22,24,26,29)(23,27,25,28)(30,32,35,31)(33,38,41,36)(34,39,42,37)(40,44,45,43);(22,23,26,25)(24,27,29,28)(30,33)(31,36)(32,38)(34,40)(35,41)(37,43)(39,44)(42,45);(18,20,21,19)(22,25,26,23)(24,28,29,27)(30,34)(31,37)(32,39)(33,40)(35,42)(36,43)(38,44)(41,45)

Conjugacy classes & character table

1496 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 27316);