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C3×C5⋊D5×D41 #27134281

order12300
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5

Aliases

direct productC3×C5⋊D5×D41
unambiguous semidirect product(C5×D41)⋊(C3×D5)

Splittings

Fitting, socle, HallC3×C52×C41 ⋊ C22
derived, HallC52×C41 ⋊ C22×C3
HallC3×C41 ⋊ C2×C5⋊D5
HallC3×C52 ⋊ C2×D41
SylowC41 ⋊ C2×C3×C5⋊D5
SylowC52 ⋊ C2×C3×D41

Subgroups

subgroupG/H
center, hypercenterC3C5⋊D5×D41
commutator, cosocle, hypocenterC52×C41C22×C3
FrattiniC1G
Fitting, socleC3×C52×C41C22
LCSG ▷ C52×C41
UCSC1 ◁ C3

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

924 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD41×(C5⋊D5)⋊C9, C9×C5⋊D5×D41, C3×D41×(C5⋊D5)⋊C3, …
maximal normal subgroup ofD41×(C5⋊D5)⋊C9, C9×C5⋊D5×D41, C3×D41×(C5⋊D5)⋊C3, …
maximal quotient ofC9×C5⋊D5×D41, C32×C5⋊D5×D41, C3×D41×C3⋊(C5⋊D5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12300, 143);