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C5×C7×Dic31 #16864677

order4340
isoclinismisoclinic class of D31
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×Dic31

Splittings

derived, SylowC31 ⋊ C4×C5×C7
HallC5×C7×C31 ⋊ C4
HallC7×C31 ⋊ C4×C5
HallC5×C31 ⋊ C4×C7

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D31
commutator, hypocenterC31C4×C5×C7
FrattiniC2C5×C7×D31
Fitting, socle, prime radicalC2×C5×C7×C31C2
cosocleC2×C31C2×C5×C7
LCSG ▷ C31
UCSC1 ◁ C2×C5×C7

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 4340

A minimal faithful permutation representation — 2 generators on 47 points:

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

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C7×Dic31, C5×C7×Dic93, C5×C7×(C31⋊C3)⋊C4, …
maximal normal subgroup ofC3×C5×C7×Dic31, C5×C7×(C31⋊C3)⋊C4, C5×ΓL(1,𝔽8)×Dic31, …
maximal quotient ofC3×C5×C7×Dic31, C5×C7×Dic93, C7×C25×Dic31, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4340, 3);