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C2×C5×C3⋊D399 #37561647

order23940
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C5×C3⋊D399
unambiguous semidirect product(C2×C3)⋊(C5×D399)
unambiguous semidirect product(C2×C7)⋊(C5×C3⋊D57)
unambiguous semidirect product(C2×C19)⋊(C5×C3⋊D21)

Splittings

Fitting, socleC2×C32×C5×C7×C19 ⋊ C2
derived, HallC32×C7×C19 ⋊ C22×C5
HallC32×C5×C7×C19 ⋊ C22
HallC32×C5×C19 ⋊ C2×D7
HallC5×C7×C19 ⋊ C2×C3⋊D3
HallC32×C5×C7 ⋊ C2×D19
HallC32×C19 ⋊ C2×C5×D7
HallC7×C19 ⋊ C2×C5×C3⋊D3
HallC5×C19 ⋊ C2×C3⋊D21
HallC32×C7 ⋊ C2×C5×D19
HallC32×C5 ⋊ C2×D133
HallC5×C7 ⋊ C2×C3⋊D57
SylowC19 ⋊ C2×C5×C3⋊D21
SylowC32 ⋊ C2×C5×D133
SylowC7 ⋊ C2×C5×C3⋊D57

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊D399
commutator, cosocle, hypocenterC32×C7×C19C22×C5
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C19C2
LCSG ▷ C32×C7×C19
UCSC1 ◁ C2×C5

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 11970

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

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

Conjugacy classes & character table

6000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 779);