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C43×#494 #14582525

order2752
nilpotency class3
isoclinismisoclinic class of #465
automorphism?
homologyAbelianization (H1) = C23×C43 · Schur multiplier (H2) = C2×C4

Aliases

direct productC43×#494

Subgroups

subgroupG/H
center, socle, prime radicalC22×C43C2×D4
commutator, Frattini, cosocleC2×C4C23×C43
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C42×C43 ◁ G

122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 63
transitive degreeμt(G) = 2752

A minimal faithful permutation representation — 3 generators on 63 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)(45,47)(48,49,52,55)(50,56,59,63)(51,60,57,54)(53,61,62,58);(48,50,57,61,52,59,51,58)(49,53,60,63,55,62,54,56);(44,45,46,47)

Conjugacy classes & character table

946 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC43×#1358, C43×#1362, C43×#1411, …
maximal normal subgroup ofC43×#1358, C43×#1362, C43×#1411, …
maximal quotient ofC43×#1707, C43×#1710, C43×#1713, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 175);