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C41×#1039⋊C3 #27134197

order12300
isoclinismisoclinic class of (C5⋊D5)⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C41 · Schur multiplier (H2) = C5

Aliases

direct productC41×#1039⋊C3
unambiguous semidirect product#1039⋊(C3×C41)
unambiguous semidirect product(C41×#1039)⋊C3

Splittings

derived, SylowC52 ⋊ C3×C4×C41
HallC41×#1039 ⋊ C3
HallC41×C52⋊C3 ⋊ C4
HallC52×C41 ⋊ C3×C4
Hall#1039 ⋊ C3×C41
HallC52⋊C3 ⋊ C4×C41

Subgroups

subgroupG/H
center, hypercenterC2×C41(C5⋊D5)⋊C3
commutator, hypocenterC52C3×C4×C41
FrattiniC2C41×(C5⋊D5)⋊C3
Fitting, socleC2×C52×C41C2×C3
prime radicalC2×C41×C52⋊C3C2
cosocleC2×C52C2×C3×C41
LCSG ▷ C52
UCSC1 ◁ C2×C41

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

820 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C41×#1039⋊C3, C41×C3⋊(#1039⋊C3)
maximal normal subgroup ofC3×C41×#1039⋊C3
maximal quotient ofC41×#1039⋊C9, C3×C41×#1039⋊C3, C41×C3⋊(#1039⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12300, 59);