Finite Group Databasebeta

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C32×D5×C11×D19 #49178662

order37620
automorphism?
homologyAbelianization (H1) = C22×C32×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC32×D5×C11×D19

Splittings

Fitting, socle, HallC32×C5×C11×C19 ⋊ C22
derived, HallC5×C19 ⋊ C22×C32×C11
HallC32×C11×C19 ⋊ C2×D5
HallC5×C11×C19 ⋊ C22×C32
HallC32×C5×C19 ⋊ C22×C11
HallC32×C5×C11 ⋊ C2×D19
HallC11×C19 ⋊ C2×C32×D5
HallC32×C19 ⋊ C2×D5×C11
HallC5×C11 ⋊ C2×C32×D19
HallC32×C5 ⋊ C2×C11×D19
SylowC19 ⋊ C2×C32×D5×C11
SylowC5 ⋊ C2×C32×C11×D19

Subgroups

subgroupG/H
center, hypercenterC32×C11D5×D19
commutator, cosocle, hypocenterC5×C19C22×C32×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C19C22
LCSG ▷ C5×C19
UCSC1 ◁ C32×C11

240 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 120 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) = 9405

Conjugacy classes & character table

4356 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 371);