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C52×C7×H(3,𝔽5) #36346261

order21875
nilpotency class2
automorphism?
homologyAbelianization (H1) = C54×C7 · Schur multiplier (H2) = C57

Aliases

direct productC52×C7×H(3,𝔽5)
unambiguous semidirect productC52⋊(C53×C7)
unambiguous semidirect product(C52×C7)⋊C53

Subgroups

subgroupG/H
center, socleC53×C7C52
commutator, Frattini, cosocleC5C54×C7
LCSG ▷ C5 ▷ C1
UCSC1 ◁ C53×C7 ◁ G

4752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 4375

A minimal faithful permutation representation — 4 generators on 42 points:

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

Conjugacy classes & character table

5075 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21875, 72);