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C5⋊(C47⋊(D19⋊C3)) #40999552

order26790
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC5⋊(C47⋊(D19⋊C3))
unambiguous semidirect productC47⋊(C5⋊(D19⋊C3))
unambiguous semidirect product(C19⋊C3)⋊D235
unambiguous semidirect productD4465⋊C3

Splittings

Fitting, socle, derived, HallC5×C19×C47 ⋊ C2×C3
HallC5×C47×C19⋊C3 ⋊ C2
HallD4465 ⋊ C3
HallC47×C19⋊C3 ⋊ D5
HallC19×C47 ⋊ C3×D5
HallC5×C19⋊C3 ⋊ D47
HallC5×C47 ⋊ D19⋊C3
HallC5×C19 ⋊ C3×D47
HallC19⋊C3 ⋊ D235
SylowC47 ⋊ C5⋊(D19⋊C3)
SylowC19 ⋊ C3×D235
SylowC5 ⋊ C47⋊(D19⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C19×C47C2×C3
LCSG ▷ C5×C19×C47
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 71
transitive degreeμt(G) = 4465

A minimal faithful permutation representation — 2 generators on 71 points:

(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)(49,53,54,50,51,55)(52,61,58,56,57,63)(59,64,66,65,62,60)(68,69)(70,71);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(48,49,52,58,64,61,65,51,55,60,66,54,53,59,57,62,63,56,50)(67,68,70,71,69)

Polycyclic presentation:

2,3,5,19,47|c^a=c^4,d^a=d^18,e^a=e^46,d^b=d^7

Conjugacy classes & character table

1062 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26790, 24);