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C11⋊((C61⋊C3)⋊D7) #43245341

order28182
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC11⋊((C61⋊C3)⋊D7)
unambiguous semidirect product(C61⋊C3)⋊D77

Splittings

Fitting, socle, derived, HallC7×C11×C61 ⋊ C2×C3
HallC7×C11×C61⋊C3 ⋊ C2
HallD4697 ⋊ C3
HallC11×C61⋊C3 ⋊ D7
HallC7×C61⋊C3 ⋊ D11
HallC11×C61 ⋊ C3×D7
HallC7×C61 ⋊ C3×D11
HallC61⋊C3 ⋊ D77
HallC7×C11 ⋊ D61⋊C3
SylowC61 ⋊ C3×D77
SylowC11 ⋊ (C61⋊C3)⋊D7
SylowC7 ⋊ C11⋊(D61⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C61C2×C3
LCSG ▷ C7×C11×C61
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 79
transitive degreeμt(G) = 4697

A minimal faithful permutation representation — 2 generators on 79 points:

(2,3)(4,5)(6,7)(9,10)(11,12)(13,14)(15,16)(17,18)(20,24,25,21,22,26)(23,32,33,27,28,42)(29,45,46,35,36,58)(30,44,40,38,34,31)(37,63,64,48,49,74)(39,61,62,50,47,55)(41,43,60,52,53,56)(51,76,77,66,65,72)(54,59,75,68,67,73)(57,79,78,70,71,69);(1,2,4,6,7,5,3)(8,9,11,13,15,17,18,16,14,12,10)(19,20,23,29,37,49,65,71,73,74,68,52,40,25,24,30,39,51,67,36,47,56,58,72,78,62,33,44,32,43,57,70,53,28,34,42,55,69,77,46,60,61,45,59,66,50,38,22,26,31,41,54,64,75,79,76,63,48,35,27,21)

Polycyclic presentation:

2,3,7,11,61|c^a=c^6,d^a=d^10,e^a=e^60,e^b=e^47

Conjugacy classes & character table

890 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28182, 45);