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Dic5×C67⋊C3 #16860839

order4020
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productDic5×C67⋊C3
unambiguous semidirect product(Dic5×C67)⋊C3

Splittings

derived, HallC5×C67 ⋊ C3×C4
HallDic5×C67 ⋊ C3
HallC5×C67⋊C3 ⋊ C4
SylowC67 ⋊ C3×Dic5
SylowC5 ⋊ C4×C67⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D5×C67⋊C3
commutator, hypocenterC5×C67C3×C4
Fitting, socle, cosocleC2×C5×C67C2×C3
prime radicalC2×C5×C67⋊C3C2
LCSG ▷ C5×C67
UCSC1 ◁ C2

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 76
transitive degreeμt(G) = 1340

A minimal faithful permutation representation — 2 generators on 76 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)(34,46,52)(37,48,56)(40,51,53)(43,54,50)(45,57,47)(49,61,63)(55,65,64)(58,67,62)(59,66,60)(68,72,71)(69,73,70)(74,76,75);(1,3,2,4)(6,9)(7,8)(10,11,13,17,24,34,36,16,22,30,40,52,63,61,33,45,58,68,73,57,31,41,53,64,71,75,72,54,29,14,18,25,35,47,60,51,26,12,15,20,27,37,49,48,23,32,43,55,66,44,56,46,59,69,74,76,67,42,21,28,38,50,62,70,65,39,19)

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×Dic5×C67⋊C3, Dic15×C67⋊C3, Dic25×C67⋊C3, …
maximal normal subgroup ofC3×Dic5×C67⋊C3, C5×Dic5×C67⋊C3, C7×Dic5×C67⋊C3
maximal quotient ofDic5×C67⋊C9, C3×Dic5×C67⋊C3, Dic15×C67⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4020, 11);