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C3⋊(Dic11⋊C5) #10620333

order660
isoclinismisoclinic class of C3⋊AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊Dic3
unambiguous semidirect productDic33⋊C5

Splittings

derived, HallC3×C11 ⋊ C4×C5
HallC3×C11⋊C5 ⋊ C4
HallDic33 ⋊ C5
HallC11⋊C5 ⋊ Dic3
SylowC11 ⋊ C5×Dic3
SylowC3 ⋊ Dic11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C3⋊AGL(1,𝔽11)
commutator, hypocenterC3×C11C4×C5
Fitting, socle, cosocleC2×C3×C11C2×C5
prime radicalC2×C3×C11⋊C5C2
LCSG ▷ C3×C11
UCSC1 ◁ C2

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 132

Polycyclic presentation:

2,5,2,3,11|a^2=c,d^a=d^2,e^a=e^10,e^b=e^4

Conjugacy classes & character table

36 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic3×AGL(1,𝔽11), D3×Dic11⋊C5, #63140⋊C5, …
maximal normal subgroup ofDic3×AGL(1,𝔽11), D3×Dic11⋊C5, #63140⋊C5, …
maximal quotient ofC3⋊((C11⋊C5)⋊C8), C2×C3⋊(Dic11⋊C5), C9⋊(Dic11⋊C5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(660, 3);