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C32×#4223 #13093283

order1476
isoclinismisoclinic class of #4223
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC32×#4223

Splittings

Fitting, socle, HallC32×C41 ⋊ C4
derived, SylowC41 ⋊ C32×C4

Subgroups

subgroupG/H
center, hypercenterC32#4223
commutator, hypocenterC41C32×C4
FrattiniC1G
Fitting, socleC32×C41C4
prime radicalC32×D41C2
cosocleD41C2×C32
LCSG ▷ C41
UCSC1 ◁ C32

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 369

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

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

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×C11×#4223, C32×C11⋊#4223, C3×#14523821⋊C3, …
maximal normal subgroup ofC32×C11×#4223, C32×C13×#4223, C32×C17×#4223, …
maximal quotient ofC32×C11×#4223, C32×C11⋊#4223, C3×#14523821⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1476, 19);