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C5×(Dic61⋊C3)⋊C5 #32912949

order18300
automorphism?
homologyAbelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×(Dic61⋊C3)⋊C5
unambiguous semidirect product(Dic61⋊C3)⋊C52
unambiguous semidirect product(Dic61⋊C5)⋊(C3×C5)
unambiguous semidirect product(C5×Dic61⋊C3)⋊C5
unambiguous semidirect product(C5×Dic61⋊C5)⋊C3

Splittings

derived, SylowC61 ⋊ C3×C4×C52
HallC5×Dic61⋊C5 ⋊ C3
HallC5×(C61⋊C3)⋊C5 ⋊ C4
HallC5×C61⋊C5 ⋊ C3×C4
HallDic61⋊C3 ⋊ C52
HallDic61 ⋊ C3×C52
HallC61⋊C3 ⋊ C4×C52

Subgroups

subgroupG/H
center, hypercenterC2×C5(D61⋊C3)⋊C5
commutator, hypocenterC61C3×C4×C52
FrattiniC2C5×(D61⋊C3)⋊C5
Fitting, socleC2×C5×C61C2×C3×C5
prime radicalC2×C5×(C61⋊C3)⋊C5C2
cosocleC2×C61C2×C3×C52
LCSG ▷ C61
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1220

Conjugacy classes & character table

320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18300, 72);