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C32×C4×C5×C7×C11 #28357472

order13860
nilpotency class1
isoclinismisoclinic class of C1
automorphism?
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3

Aliases

abelianC32×C4×C5×C7×C11

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C2×C32×C5×C7×C11
socle, prime radicalC2×C32×C5×C7×C11C2
LCSG ▷ C1
UCSC1 ◁ G

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 13860

A minimal faithful permutation representation — 2 generators on 33 points:

(1,2,3,4)(5,6,7)(11,12,13,14,15)(16,17,18,19,20,21,22)(23,24,25,26,27,28,29,30,31,32,33);(8,9,10)

Conjugacy classes & character table

13860 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C5×C7×C8×C11, C2×C32×C4×C5×C7×C11
maximal normal subgroup ofC32×C5×C7×C8×C11, C2×C32×C4×C5×C7×C11
maximal quotient ofC32×C5×C7×C8×C11, C2×C32×C4×C5×C7×C11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 139);