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C2×C5×C3⋊D429 #38788319

order25740
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C5×C3⋊D429
unambiguous semidirect product(C2×C3)⋊(C5×D429)
unambiguous semidirect product(C2×C13)⋊(C5×C3⋊D33)

Splittings

Fitting, socleC2×C32×C5×C11×C13 ⋊ C2
derived, HallC32×C11×C13 ⋊ C22×C5
HallC32×C5×C11×C13 ⋊ C22
HallC5×C11×C13 ⋊ C2×C3⋊D3
HallC32×C5×C13 ⋊ C2×D11
HallC32×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C5×C3⋊D3
HallC32×C13 ⋊ C2×C5×D11
HallC32×C11 ⋊ C2×C5×D13
HallC5×C13 ⋊ C2×C3⋊D33
HallC5×C11 ⋊ C2×C3⋊D39
HallC32×C5 ⋊ C2×D143
SylowC13 ⋊ C2×C5×C3⋊D33
SylowC11 ⋊ C2×C5×C3⋊D39
SylowC32 ⋊ C2×C5×D143

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊D429
commutator, cosocle, hypocenterC32×C11×C13C22×C5
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C13C2
LCSG ▷ C32×C11×C13
UCSC1 ◁ C2×C5

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 12870

A minimal faithful permutation representation — 3 generators on 37 points:

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

Conjugacy classes & character table

6450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 550);