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C4×C5×C79⋊C3 #18011602

order4740
isoclinismisoclinic class of C79⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C79⋊C3
unambiguous semidirect product(C4×C79)⋊(C3×C5)
unambiguous semidirect product(C4×C5×C79)⋊C3

Splittings

Fitting, HallC4×C5×C79 ⋊ C3
derived, SylowC79 ⋊ C3×C4×C5
HallC5×C79 ⋊ C3×C4
HallC4×C79 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC4×C5C79⋊C3
commutator, hypocenterC79C3×C4×C5
FrattiniC2C2×C5×C79⋊C3
FittingC4×C5×C79C3
socleC2×C5×C79C2×C3
prime radicalC2×C5×C79⋊C3C2
cosocleC2×C79C2×C3×C5
LCSG ▷ C79
UCSC1 ◁ C4×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 88
transitive degreeμt(G) = 1580

A minimal faithful permutation representation — 2 generators on 88 points:

(1,2,3,4)(5,6,7,8,9)(11,12,14)(13,16,21)(15,19,18)(17,23,31)(20,26,28)(22,29,25)(24,33,44)(27,36,41)(30,39,38)(32,42,35)(34,46,59)(37,49,57)(40,52,54)(43,55,51)(45,47,48)(50,62,72)(53,65,70)(56,68,67)(58,63,64)(60,73,61)(66,74,81)(69,77,79)(71,75,76)(78,82,86)(80,83,84)(85,87,88);(10,11,13,17,24,34,47,31,41,54,67,76,62,33,45,58,71,80,85,87,77,52,26,12,15,20,27,37,50,63,42,21,28,38,51,64,46,60,59,72,81,86,88,82,65,36,16,22,30,40,53,66,75,55,29,14,18,25,35,48,61,73,44,57,70,79,84,74,49,23,32,43,56,69,78,83,68,39,19)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×Dic3×C79⋊C3, C3×C4×C5×C79⋊C3, C4×C25×C79⋊C3, …
maximal normal subgroup ofC3×C4×C5×C79⋊C3, C4×C25×C79⋊C3, C4×C52×C79⋊C3, …
maximal quotient ofC4×C5×C79⋊C9, C5×Dic3×C79⋊C3, C3×C4×C5×C79⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4740, 2);