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(C5⋊(D19⋊C3))⋊D33 #49178605

order37620
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(C5⋊(D19⋊C3))⋊D33
unambiguous semidirect product(D95⋊D33)⋊C3

Splittings

Fitting, socle, derivedC3×C5×C11×C19 ⋊ C22×C3
HallC3×C5×C11×C19⋊C3 ⋊ C22
HallC3×C11×C19⋊C3 ⋊ C2×D5
HallC5×C11×C19 ⋊ C2×C3×D3
HallC3×C5×C19⋊C3 ⋊ C2×D11
HallC11×C19 ⋊ C3×D3×D5
HallC3×C19⋊C3 ⋊ D5×D11
HallC5×C19 ⋊ C2×C3×D33
HallC5×C11 ⋊ D3×D19⋊C3
SylowC19 ⋊ C3×D5×D33
SylowC11 ⋊ D15⋊(D19⋊C3)
SylowC5 ⋊ D33×D19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C19C22×C3
LCSG ▷ C3×C5×C11×C19
UCSC1

176 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Polycyclic presentation:

2^2,3^2,5,11,19|e^a=e^4,g^a=g^18,d^b=d^2,e^b=e^4,f^b=f^10,g^c=g^7

Conjugacy classes & character table

468 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 314);