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C4×C52×C67⋊C3 #34117201

order20100
isoclinismisoclinic class of C67⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC4×C52×C67⋊C3
unambiguous semidirect product(C4×C67)⋊(C3×C52)
unambiguous semidirect product(C4×C5×C67)⋊(C3×C5)

Splittings

Fitting, HallC4×C52×C67 ⋊ C3
derived, SylowC67 ⋊ C3×C4×C52
HallC52×C67 ⋊ C3×C4
HallC4×C67 ⋊ C3×C52

Subgroups

subgroupG/H
center, hypercenterC4×C52C67⋊C3
commutator, hypocenterC67C3×C4×C52
FrattiniC2C2×C52×C67⋊C3
FittingC4×C52×C67C3
socleC2×C52×C67C2×C3
prime radicalC2×C52×C67⋊C3C2
cosocleC2×C67C2×C3×C52
LCSG ▷ C67
UCSC1 ◁ C4×C52

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 81
transitive degreeμt(G) = 6700

A minimal faithful permutation representation — 2 generators on 81 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)(77,78,79,80,81);(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)(72,73,74,75,76)

Conjugacy classes & character table

2500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20100, 57);