Finite Group Databasebeta

← Prev (#49115026) Next (#49115028) →

C2×C7×C3⋊D429 #49115027

order36036
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C7×C3⋊D429
unambiguous semidirect product(C2×C3)⋊(C7×D429)
unambiguous semidirect product(C2×C11)⋊(C7×C3⋊D39)
unambiguous semidirect product(C2×C13)⋊(C7×C3⋊D33)

Splittings

Fitting, socleC2×C32×C7×C11×C13 ⋊ C2
derived, HallC32×C11×C13 ⋊ C22×C7
HallC32×C7×C11×C13 ⋊ C22
HallC7×C11×C13 ⋊ C2×C3⋊D3
HallC32×C7×C13 ⋊ C2×D11
HallC32×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C7×C3⋊D3
HallC32×C13 ⋊ C2×C7×D11
HallC32×C11 ⋊ C2×C7×D13
HallC7×C13 ⋊ C2×C3⋊D33
HallC7×C11 ⋊ C2×C3⋊D39
HallC32×C7 ⋊ C2×D143
SylowC13 ⋊ C2×C7×C3⋊D33
SylowC11 ⋊ C2×C7×C3⋊D39
SylowC32 ⋊ C2×C7×D143

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊D429
commutator, cosocle, hypocenterC32×C11×C13C22×C7
FrattiniC1G
Fitting, socleC2×C32×C7×C11×C13C2
LCSG ▷ C32×C11×C13
UCSC1 ◁ C2×C7

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

Conjugacy classes & character table

9030 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 695);