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C2×C7×C3⋊D435 #49141693

order36540
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C7×C3⋊D435
unambiguous semidirect product(C2×C3)⋊(C7×D435)
unambiguous semidirect product(C2×C5)⋊(C7×C3⋊D87)

Splittings

Fitting, socleC2×C32×C5×C7×C29 ⋊ C2
derived, HallC32×C5×C29 ⋊ C22×C7
HallC32×C5×C7×C29 ⋊ C22
HallC32×C7×C29 ⋊ C2×D5
HallC5×C7×C29 ⋊ C2×C3⋊D3
HallC32×C5×C7 ⋊ C2×D29
HallC32×C29 ⋊ C2×C7×D5
HallC7×C29 ⋊ C2×C3⋊D15
HallC5×C29 ⋊ C2×C7×C3⋊D3
HallC32×C7 ⋊ C2×D145
HallC32×C5 ⋊ C2×C7×D29
HallC5×C7 ⋊ C2×C3⋊D87
SylowC29 ⋊ C2×C7×C3⋊D15
SylowC32 ⋊ C2×C7×D145
SylowC5 ⋊ C2×C7×C3⋊D87

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊D435
commutator, cosocle, hypocenterC32×C5×C29C22×C7
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C29C2
LCSG ▷ C32×C5×C29
UCSC1 ◁ C2×C7

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 49
transitive degreeμt(G) = 18270

A minimal faithful permutation representation — 3 generators on 49 points:

(4,5)(7,8)(10,11)(12,13)(14,15,16,17,18,19,20)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49);(1,2)(6,7,8)(9,10,12,13,11)(21,22,24,26,28,30,32,34,36,38,40,42,44,46,48,49,47,45,43,41,39,37,35,33,31,29,27,25,23);(3,4,5)

Conjugacy classes & character table

9156 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 535);