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C54×C23 #28385477

order14375
nilpotency class1
isoclinismisoclinic class of C1
automorphism?
homologyAbelianization (H1) = G · Schur multiplier (H2) = C56

Aliases

abelianC54×C23

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

2240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 14375

A minimal faithful permutation representation — 4 generators on 43 points:

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

Conjugacy classes & character table

14375 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C54×C23
maximal normal subgroup ofC2×C54×C23
maximal quotient ofC2×C54×C23

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14375, 15);