Finite Group Databasebeta

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C43×#469 #14582500

order2752
nilpotency class3
isoclinismisoclinic class of #468
automorphism?
homologyAbelianization (H1) = C23×C43 · Schur multiplier (H2) = C2×C4

Aliases

direct productC43×#469

Subgroups

subgroupG/H
center, socleC22×C43C2×D4
commutator, Frattini, cosocleC2×C4C23×C43
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C22×C4×C43 ◁ G

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 55
transitive degreeμt(G) = 1376

A minimal faithful permutation representation — 3 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43)(44,45)(46,47)(49,52)(50,53)(54,55);(48,49,53,55,51,54,50,52);(45,47)(49,54)(52,55)

Conjugacy classes & character table

688 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC43×#1339, C43×#1341, C43×#2190, …
maximal normal subgroup ofC43×#1339, C43×#1341, C43×#2190, …
maximal quotient ofC43×#1687, C43×#1688, C43×#1693, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 150);