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C2×C5×C3⋊D231 #28357779

order13860
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C5×C3⋊D231
unambiguous semidirect product(C2×C3)⋊(C5×D231)
unambiguous semidirect product(C2×C7)⋊(C5×C3⋊D33)

Splittings

Fitting, socleC2×C32×C5×C7×C11 ⋊ C2
derived, HallC32×C7×C11 ⋊ C22×C5
HallC32×C5×C7×C11 ⋊ C22
HallC32×C5×C11 ⋊ C2×D7
HallC5×C7×C11 ⋊ C2×C3⋊D3
HallC32×C5×C7 ⋊ C2×D11
HallC32×C11 ⋊ C2×C5×D7
HallC7×C11 ⋊ C2×C5×C3⋊D3
HallC32×C7 ⋊ C2×C5×D11
HallC5×C11 ⋊ C2×C3⋊D21
HallC32×C5 ⋊ C2×D77
HallC5×C7 ⋊ C2×C3⋊D33
SylowC11 ⋊ C2×C5×C3⋊D21
SylowC32 ⋊ C2×C5×D77
SylowC7 ⋊ C2×C5×C3⋊D33

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊D231
commutator, cosocle, hypocenterC32×C7×C11C22×C5
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C11C2
LCSG ▷ C32×C7×C11
UCSC1 ◁ C2×C5

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 6930

A minimal faithful permutation representation — 3 generators on 31 points:

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

Conjugacy classes & character table

3480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 446);