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D33⋊D33 #17983783

order4356
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productD33⋊D33

Splittings

Fitting, socle, derived, HallC32×C112 ⋊ C22
SylowC112 ⋊ D32
SylowC32 ⋊ D112

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C112C22
LCSG ▷ C32×C112
UCSC1

133 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 132

Polycyclic presentation:

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

Conjugacy classes & character table

309 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#36345109, #36345119, (C3⋊AGL(1,𝔽11))⋊D33, …
maximal normal subgroup of#36345119, (C3⋊AGL(1,𝔽11))⋊D33, #36345134, …
maximal quotient ofC5×D33⋊D33, D33⋊D165, #36345336, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4356, 110);