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C5×C23×H(3,𝔽5) #28385474

order14375
nilpotency class2
isoclinismisoclinic class of H(3,𝔽5)
automorphism?
homologyAbelianization (H1) = C53×C23 · Schur multiplier (H2) = C54

Aliases

direct productC5×C23×H(3,𝔽5)
unambiguous semidirect productC52⋊(C52×C23)
unambiguous semidirect product(C52×C23)⋊C52

Subgroups

subgroupG/H
center, socleC52×C23C52
commutator, Frattini, cosocleC5C53×C23
LCSG ▷ C5 ▷ C1
UCSC1 ◁ C52×C23 ◁ G

260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 2875

A minimal faithful permutation representation — 3 generators on 53 points:

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

Conjugacy classes & character table

3335 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14375, 12);