Finite Group Databasebeta

← Prev (#11925954) Next (#11925956) →

C5×#6882 #11925955

order1215
nilpotency class4
isoclinismisoclinic class of #6881
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×#6882

Subgroups

subgroupG/H
center, socleC3×C5#732
commutator, Frattini, cosocleC3×C9C32×C5
prime radicalC32×C5H(3,𝔽3)
LCSG ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1
UCSC1 ◁ C3×C5 ◁ C32×C5 ◁ C3×C5×C9 ◁ G

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 135

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

95 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×#6882, C5×#10624845, C5×#10624847, …
maximal normal subgroup ofC3×C5×#6882, C5×#10624845, C5×#10624847, …
maximal quotient ofC5×#10624482, C5×#10624483, C5×#10624490, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1215, 29);