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C2×C5⋊(C23⋊(D19⋊C3)) #39910751

order26220
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊(C23⋊(D19⋊C3))
unambiguous semidirect product(C2×C5)⋊(C23⋊(D19⋊C3))
unambiguous semidirect product(C2×C23)⋊(C5⋊(D19⋊C3))
unambiguous semidirect product(C2×C19⋊C3)⋊D115
unambiguous semidirect product(C2×D2185)⋊C3

Splittings

Fitting, socleC2×C5×C19×C23 ⋊ C2×C3
derived, HallC5×C19×C23 ⋊ C22×C3
HallC2×D2185 ⋊ C3
HallC5×C23×C19⋊C3 ⋊ C22
HallC23×C19⋊C3 ⋊ C2×D5
HallC19×C23 ⋊ C2×C3×D5
HallC5×C19⋊C3 ⋊ C2×D23
HallC5×C23 ⋊ C2×D19⋊C3
HallC5×C19 ⋊ C2×C3×D23
HallC19⋊C3 ⋊ C2×D115
SylowC23 ⋊ C2×C5⋊(D19⋊C3)
SylowC19 ⋊ C2×C3×D115
SylowC5 ⋊ C2×C23⋊(D19⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(C23⋊(D19⋊C3))
commutator, cosocle, hypocenterC5×C19×C23C22×C3
FrattiniC1G
Fitting, socleC2×C5×C19×C23C2×C3
LCSG ▷ C5×C19×C23
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4370

Conjugacy classes & character table

1044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 41);