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Dic1395 #19150029

order5580
automorphismAut(G) order 2008800
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic1395
unambiguous semidirect productC9⋊Dic155
unambiguous semidirect productC31⋊Dic45

Splittings

derived, HallC5×C9×C31 ⋊ C4
HallC9×C31 ⋊ Dic5
HallC5×C31 ⋊ Dic9
HallC5×C9 ⋊ Dic31
SylowC31 ⋊ Dic45
SylowC9 ⋊ Dic155
SylowC5 ⋊ Dic279

Subgroups

subgroupG/H
center, hypercenterC2D1395
commutator, hypocenterC5×C9×C31C4
FrattiniC2×C3D465
FittingC2×C5×C9×C31C2
socleC2×C3×C5×C31D3
LCSG ▷ C5×C9×C31
UCSC1 ◁ C2

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,5,31,2,3|a^2=e,b^3=f^2,b^a=b^2f,c^a=c^4,d^a=d^30,f^a=f^2

Conjugacy classes & character table

1398 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofDic6975, C9⋊(ΓL(1,𝔽32)⋊Dic5), C5×Dic1395, …
maximal normal subgroup ofC9⋊(ΓL(1,𝔽32)⋊Dic5), C5×Dic1395, Dic2790
maximal quotient ofDic6975, C5×Dic1395, C9⋊(C31⋊#1039), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5580, 18);