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C2×C11×C3⋊D183 #37563569

order24156
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C11×C3⋊D183
unambiguous semidirect product(C2×C3)⋊(C11×D183)
unambiguous semidirect product(C2×C61)⋊(C11×C3⋊D3)

Splittings

Fitting, socleC2×C32×C11×C61 ⋊ C2
derived, HallC32×C61 ⋊ C22×C11
HallC32×C11×C61 ⋊ C22
HallC11×C61 ⋊ C2×C3⋊D3
HallC32×C11 ⋊ C2×D61
SylowC61 ⋊ C2×C11×C3⋊D3
SylowC32 ⋊ C2×C11×D61

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊D183
commutator, cosocle, hypocenterC32×C61C22×C11
FrattiniC1G
Fitting, socleC2×C32×C11×C61C2
LCSG ▷ C32×C61
UCSC1 ◁ C2×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 80
transitive degreeμt(G) = 12078

A minimal faithful permutation representation — 3 generators on 80 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)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63,64,65,66,67,68,69,70,71,72)(74,75)(77,78);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(76,77,78)(79,80);(73,74,75)

Conjugacy classes & character table

6072 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24156, 127);