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C2×C3×C29×(C5⋊D5)⋊C3 #39908069

order26100
automorphism?
homologyAbelianization (H1) = C22×C32×C29 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC2×C3×C29×(C5⋊D5)⋊C3
unambiguous semidirect product(C2×C5⋊D5)⋊(C32×C29)
unambiguous semidirect product(C2×C3×C5⋊D5)⋊(C3×C29)
unambiguous semidirect product(C2×C29×C5⋊D5)⋊C32
unambiguous semidirect product(C2×C3×C29×C5⋊D5)⋊C3

Splittings

Fitting, socleC2×C3×C52×C29 ⋊ C2×C3
derived, SylowC52 ⋊ C22×C32×C29
HallC3×C29×C52⋊C3 ⋊ C22
HallC2×C29×C5⋊D5 ⋊ C32
HallC52×C29 ⋊ C22×C32
HallC3×C52⋊C3 ⋊ C22×C29
HallC2×C5⋊D5 ⋊ C32×C29

Subgroups

subgroupG/H
center, hypercenterC2×C3×C29(C5⋊D5)⋊C3
commutator, cosocle, hypocenterC52C22×C32×C29
FrattiniC1G
Fitting, socleC2×C3×C52×C29C2×C3
LCSG ▷ C52
UCSC1 ◁ C2×C3×C29

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2610

Conjugacy classes & character table

1740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 303);