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C4×(C61⋊C3)⋊C5 #16814550

order3660
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×(C61⋊C3)⋊C5
unambiguous semidirect product(C4×C61⋊C3)⋊C5
unambiguous semidirect product(C4×C61⋊C5)⋊C3

Splittings

Fitting, HallC4×C61 ⋊ C3×C5
derived, SylowC61 ⋊ C3×C4×C5
HallC4×C61⋊C5 ⋊ C3
HallC4×C61⋊C3 ⋊ C5
HallC61⋊C5 ⋊ C3×C4
HallC61⋊C3 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC4(C61⋊C3)⋊C5
commutator, hypocenterC61C3×C4×C5
FrattiniC2C2×(C61⋊C3)⋊C5
FittingC4×C61C3×C5
socle, cosocleC2×C61C2×C3×C5
prime radicalC2×(C61⋊C3)⋊C5C2
LCSG ▷ C61
UCSC1 ◁ C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 65
transitive degreeμt(G) = 244

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic3×(C61⋊C3)⋊C5, C3×C4×(C61⋊C3)⋊C5, Dic5×(C61⋊C3)⋊C5, …
maximal normal subgroup ofC3×C4×(C61⋊C3)⋊C5, C4×C5×(C61⋊C3)⋊C5, C4×C7×(C61⋊C3)⋊C5
maximal quotient ofC4×(C61⋊C5)⋊C9, Dic3×(C61⋊C3)⋊C5, C3×C4×(C61⋊C3)⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3660, 3);