Finite Group Databasebeta

← Prev (#34117248) Next (#34117250) →

C2×C5×D5×C67⋊C3 #34117249

order20100
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D5×C67⋊C3
unambiguous semidirect productC5⋊(C22×C5×C67⋊C3)
unambiguous semidirect product(C2×C5)⋊(C2×C5×C67⋊C3)
unambiguous semidirect product(C2×D5×C67)⋊(C3×C5)
unambiguous semidirect product(C2×C5×D5×C67)⋊C3

Splittings

Fitting, socleC2×C52×C67 ⋊ C2×C3
derivedC5×C67 ⋊ C22×C3×C5
HallC2×C5×D5×C67 ⋊ C3
HallC52×C67⋊C3 ⋊ C22
HallC52×C67 ⋊ C22×C3
SylowC67 ⋊ C2×C3×C5×D5
SylowC52 ⋊ C22×C67⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5D5×C67⋊C3
commutator, cosocle, hypocenterC5×C67C22×C3×C5
FrattiniC1G
Fitting, socleC2×C52×C67C2×C3
LCSG ▷ C5×C67
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 79
transitive degreeμt(G) = 1340

A minimal faithful permutation representation — 2 generators on 79 points:

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

Conjugacy classes & character table

1000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20100, 105);