Finite Group Databasebeta

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C41×#534 #14580002

order2624
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C24×C41 · Schur multiplier (H2) = C25

Aliases

direct productC41×#534

Subgroups

subgroupG/H
center, socleC22×C41C24
commutator, Frattini, cosocleC22C24×C41
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ G

346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 656

A minimal faithful permutation representation — 4 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41)(43,45)(46,47)(48,52)(49,50)(51,53);(47,50)(51,52);(42,43)(44,45)(46,47)(48,51)(49,50)(52,53);(46,48)(47,51)(49,53)(50,52)

Conjugacy classes & character table

902 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC41×#1595, C41×#1601, C41×#1607, …
maximal normal subgroup ofC41×#1595, C41×#1601, C41×#1607, …
maximal quotient ofC41×#2308, C41×#2315, C41×#2321, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 215);