Finite Group Databasebeta

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C27×#595 #14270100

order1836
isoclinismisoclinic class of #595
automorphism?
homologyAbelianization (H1) = C4×C27 · Schur multiplier (H2) = C1

Aliases

direct productC27×#595

Splittings

Fitting, HallC17×C27 ⋊ C4
derived, SylowC17 ⋊ C4×C27

Subgroups

subgroupG/H
center, hypercenterC27#595
commutator, hypocenterC17C4×C27
FrattiniC9C3×#595
FittingC17×C27C4
socleC3×C17C4×C9
prime radicalC3×D17C2×C9
cosocleC9×D17C2×C3
LCSG ▷ C17
UCSC1 ◁ C27

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 459

A minimal faithful permutation representation — 2 generators on 44 points:

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

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1836, 5);