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C2×C3×C5×C41⋊C5 #20259651

order6150
isoclinismisoclinic class of C41⋊C5
automorphism?
homologyAbelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC2×C3×C5×C41⋊C5
unambiguous semidirect product(C2×C41)⋊(C3×C52)
unambiguous semidirect product(C2×C3×C41)⋊C52
unambiguous semidirect product(C2×C5×C41)⋊(C3×C5)
unambiguous semidirect product(C2×C3×C5×C41)⋊C5

Splittings

Fitting, socleC2×C3×C5×C41 ⋊ C5
derived, SylowC41 ⋊ C2×C3×C52
HallC2×C3×C41 ⋊ C52
HallC3×C41 ⋊ C2×C52
HallC2×C41 ⋊ C3×C52

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C41⋊C5
commutator, hypocenterC41C2×C3×C52
FrattiniC1G
Fitting, socleC2×C3×C5×C41C5
LCSG ▷ C41
UCSC1 ◁ C2×C3×C5

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

390 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×Dic41⋊C5, C3×Dic205⋊C5, C3×Dic5×C41⋊C5, …
maximal normal subgroup ofC3×C5×Dic41⋊C5, C3×Dic205⋊C5, C3×Dic5×C41⋊C5, …
maximal quotient ofC3×C4×C5×C41⋊C5, C22×C3×C5×C41⋊C5, C2×C5×C9×C41⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6150, 26);