Finite Group Databasebeta

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C2×C13×C3⋊D231 #49115030

order36036
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C13×C3⋊D231
unambiguous semidirect product(C2×C3)⋊(C13×D231)
unambiguous semidirect product(C2×C7)⋊(C13×C3⋊D33)
unambiguous semidirect product(C2×C11)⋊(C13×C3⋊D21)

Splittings

Fitting, socleC2×C32×C7×C11×C13 ⋊ C2
derived, HallC32×C7×C11 ⋊ C22×C13
HallC32×C7×C11×C13 ⋊ C22
HallC32×C11×C13 ⋊ C2×D7
HallC7×C11×C13 ⋊ C2×C3⋊D3
HallC32×C7×C13 ⋊ C2×D11
HallC11×C13 ⋊ C2×C3⋊D21
HallC32×C13 ⋊ C2×D77
HallC32×C11 ⋊ C2×C13×D7
HallC7×C13 ⋊ C2×C3⋊D33
HallC7×C11 ⋊ C2×C13×C3⋊D3
HallC32×C7 ⋊ C2×C13×D11
SylowC11 ⋊ C2×C13×C3⋊D21
SylowC32 ⋊ C2×C13×D77
SylowC7 ⋊ C2×C13×C3⋊D33

Subgroups

subgroupG/H
center, hypercenterC2×C13C3⋊D231
commutator, cosocle, hypocenterC32×C7×C11C22×C13
FrattiniC1G
Fitting, socleC2×C32×C7×C11×C13C2
LCSG ▷ C32×C7×C11
UCSC1 ◁ C2×C13

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 18018

A minimal faithful permutation representation — 3 generators on 39 points:

(4,5)(7,8)(10,11)(12,13)(14,15)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28,29,30,31,32,33,34,35,36,37,38,39);(1,2)(6,7,8)(9,10,12,14,15,13,11)(16,17,19,21,23,25,26,24,22,20,18);(3,4,5)

Conjugacy classes & character table

9048 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 698);