Finite Group Databasebeta

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C19×D33⋊D15 #49178718

order37620
automorphism?
homologyAbelianization (H1) = C22×C19 · Schur multiplier (H2) = C2

Aliases

direct productC19×D33⋊D15
unambiguous semidirect productD33⋊(C19×D15)

Splittings

Fitting, socle, HallC32×C5×C11×C19 ⋊ C22
derived, HallC32×C5×C11 ⋊ C22×C19
HallC32×C11×C19 ⋊ C2×D5
HallC5×C11×C19 ⋊ D32
HallC32×C5×C19 ⋊ C2×D11
HallC11×C19 ⋊ D3×D15
HallC32×C19 ⋊ D5×D11
HallC32×C11 ⋊ C2×D5×C19
HallC5×C19 ⋊ (C3⋊D3)⋊D11
HallC5×C11 ⋊ D32×C19
HallC32×C5 ⋊ C2×C19×D11
SylowC11 ⋊ D3×C19×D15
SylowC32 ⋊ D5×C19×D11
SylowC5 ⋊ C19×(C3⋊D3)⋊D11

Subgroups

subgroupG/H
center, hypercenterC19D33⋊D15
commutator, cosocle, hypocenterC32×C5×C11C22×C19
FrattiniC1G
Fitting, socleC32×C5×C11×C19C22
LCSG ▷ C32×C5×C11
UCSC1 ◁ C19

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 6270

Conjugacy classes & character table

2793 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 427);