Finite Group Databasebeta

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C32×D19×D35 #37561515

order23940
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC32×D19×D35

Splittings

Fitting, socle, HallC32×C5×C7×C19 ⋊ C22
derived, HallC5×C7×C19 ⋊ C22×C32
HallC32×C7×C19 ⋊ C2×D5
HallC32×C5×C19 ⋊ C2×D7
HallC32×C5×C7 ⋊ C2×D19
HallC32×C19 ⋊ C2×D35
HallC7×C19 ⋊ C2×C32×D5
HallC5×C19 ⋊ C2×C32×D7
HallC32×C7 ⋊ D5×D19
HallC32×C5 ⋊ D7×D19
HallC5×C7 ⋊ C2×C32×D19
SylowC19 ⋊ C2×C32×D35
SylowC7 ⋊ C32×D5×D19
SylowC5 ⋊ C32×D7×D19

Subgroups

subgroupG/H
center, hypercenterC32D19×D35
commutator, cosocle, hypocenterC5×C7×C19C22×C32
FrattiniC1G
Fitting, socleC32×C5×C7×C19C22
LCSG ▷ C5×C7×C19
UCSC1 ◁ C32

240 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 96 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) = 5985

Conjugacy classes & character table

1881 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 647);