Finite Group Databasebeta

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C2×C11×C3⋊D273 #49115029

order36036
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C11×C3⋊D273
unambiguous semidirect product(C2×C3)⋊(C11×D273)
unambiguous semidirect product(C2×C7)⋊(C11×C3⋊D39)
unambiguous semidirect product(C2×C13)⋊(C11×C3⋊D21)

Splittings

Fitting, socleC2×C32×C7×C11×C13 ⋊ C2
derived, HallC32×C7×C13 ⋊ C22×C11
HallC32×C7×C11×C13 ⋊ C22
HallC32×C11×C13 ⋊ C2×D7
HallC7×C11×C13 ⋊ C2×C3⋊D3
HallC32×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C3⋊D21
HallC32×C13 ⋊ C2×C11×D7
HallC32×C11 ⋊ C2×D91
HallC7×C13 ⋊ C2×C11×C3⋊D3
HallC7×C11 ⋊ C2×C3⋊D39
HallC32×C7 ⋊ C2×C11×D13
SylowC13 ⋊ C2×C11×C3⋊D21
SylowC32 ⋊ C2×C11×D91
SylowC7 ⋊ C2×C11×C3⋊D39

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊D273
commutator, cosocle, hypocenterC32×C7×C13C22×C11
FrattiniC1G
Fitting, socleC2×C32×C7×C11×C13C2
LCSG ▷ C32×C7×C13
UCSC1 ◁ C2×C11

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

Conjugacy classes & character table

9042 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 697);