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C32×C5×C27 #11925974

order1215
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 279936
homologyAbelianization (H1) = G · Schur multiplier (H2) = C33

Aliases

abelianC32×C5×C27

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C33×C5
socle, prime radicalC33×C5C9
LCSG ▷ C1
UCSC1 ◁ G

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 1215

A minimal faithful permutation representation — 3 generators on 38 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)(34,35,36,37,38);(28,29,30);(31,32,33)

Conjugacy classes & character table

1215 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×H(3,𝔽3)⋊C27, C5×3−1+2⋊C27, C5×#10624463, …
maximal normal subgroup ofC5×H(3,𝔽3)⋊C27, C5×3−1+2⋊C27, C5×#10624463, …
maximal quotient ofC3×C5×C9×C27, C3×C5×C32⋊C27, C3×C5×C9⋊C27, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1215, 48);