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C5×#63736 #13085564

order1440
isoclinismisoclinic class of #63734
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#63736

Splittings

HallC32×C5 ⋊ Q32
SylowC32 ⋊ C5×Q32

Subgroups

subgroupG/H
centerC2×C5#3774
commutator, cosocleC3⋊(C3⋊C8)C22×C5
FrattiniC4C5×GO+(4,𝔽2)
FittingC32×C4×C5D4
socle, prime radicalC2×C32×C5D8
hypercenterC4×C5GO+(4,𝔽2)
hypocenterC32C5×Q32
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C5 ◁ C4×C5

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 2 generators on 43 points:

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

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1881);