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C17×#24404 #16882148

order4352
nilpotency class3
isoclinismisoclinic class of #24404
automorphism?
homologyAbelianization (H1) = C24×C17 · Schur multiplier (H2) = C27

Aliases

direct productC17×#24404

Subgroups

subgroupG/H
center, socleC22×C17C2×#120
commutator, Frattini, cosocleC24C24×C17
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C25×C17 ◁ G

2010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 544

A minimal faithful permutation representation — 4 generators on 29 points:

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

Conjugacy classes & character table

731 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 17392);