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C5×Dic3×C41⋊C5 #27134192

order12300
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×Dic3×C41⋊C5
unambiguous semidirect productC3⋊(C4×C5×C41⋊C5)
unambiguous semidirect product(Dic3×C41)⋊C52
unambiguous semidirect product(C5×Dic3×C41)⋊C5

Splittings

derived, HallC3×C41 ⋊ C4×C52
HallC3×C5×C41⋊C5 ⋊ C4
HallDic3×C41 ⋊ C52
SylowC41 ⋊ C52×Dic3
SylowC3 ⋊ C4×C5×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C5D3×C41⋊C5
commutator, hypocenterC3×C41C4×C52
FrattiniC2C5×D3×C41⋊C5
Fitting, socleC2×C3×C5×C41C2×C5
prime radicalC2×C3×C5×C41⋊C5C2
cosocleC2×C3×C41C2×C52
LCSG ▷ C3×C41
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

390 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×Dic9×C41⋊C5, C3×C5×Dic3×C41⋊C5, C5×C3⋊Dic3×C41⋊C5
maximal normal subgroup ofC3×C5×Dic3×C41⋊C5
maximal quotient ofC5×Dic9×C41⋊C5, C3×C5×Dic3×C41⋊C5, C5×C3⋊Dic3×C41⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12300, 54);