Finite Group Databasebeta

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C3×C7×D5×D57 #37561537

order23940
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC3×C7×D5×D57
unambiguous semidirect product(C3×D5)⋊(C3×C7×D19)

Splittings

Fitting, socle, HallC32×C5×C7×C19 ⋊ C22
derivedC3×C5×C19 ⋊ C22×C3×C7
HallC32×C7×C19 ⋊ C2×D5
HallC32×C5×C19 ⋊ C22×C7
HallC5×C7×C19 ⋊ C2×C3×D3
HallC32×C5×C7 ⋊ C2×D19
HallC32×C19 ⋊ C2×C7×D5
HallC7×C19 ⋊ C3×D3×D5
HallC5×C19 ⋊ C2×C3×D3×C7
HallC32×C7 ⋊ D5×D19
HallC32×C5 ⋊ C2×C7×D19
HallC5×C7 ⋊ C2×C3×D57
SylowC19 ⋊ C3×D3×C7×D5
SylowC32 ⋊ C7×D5×D19
SylowC5 ⋊ C2×C3×C7×D57

Subgroups

subgroupG/H
center, hypercenterC3×C7D5×D57
commutator, cosocle, hypocenterC3×C5×C19C22×C3×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C19C22
LCSG ▷ C3×C5×C19
UCSC1 ◁ C3×C7

176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 3990

Conjugacy classes & character table

2520 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 669);