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Dic15×C41⋊C5 #27134194

order12300
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productDic15×C41⋊C5
unambiguous semidirect productC3⋊(Dic5×C41⋊C5)
unambiguous semidirect product(C41×Dic15)⋊C5

Splittings

derivedC3×C5×C41 ⋊ C4×C5
HallC3×C5×C41⋊C5 ⋊ C4
HallC5×C41⋊C5 ⋊ Dic3
HallC3×C41 ⋊ C5×Dic5
SylowC41 ⋊ C5×Dic15
SylowC3 ⋊ Dic5×C41⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D15×C41⋊C5
commutator, hypocenterC3×C5×C41C4×C5
Fitting, socle, cosocleC2×C3×C5×C41C2×C5
prime radicalC2×C3×C5×C41⋊C5C2
LCSG ▷ C3×C5×C41
UCSC1 ◁ C2

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic45×C41⋊C5, C3×Dic15×C41⋊C5, C3⋊Dic15×C41⋊C5
maximal normal subgroup ofC3×Dic15×C41⋊C5
maximal quotient ofDic45×C41⋊C5, C3×Dic15×C41⋊C5, C3⋊Dic15×C41⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12300, 56);