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C32×#16811774 #44501791

order30690
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×#16811774

Splittings

Fitting, socle, HallC32×C11×C31 ⋊ C2×C5
derived, HallC11×C31 ⋊ C2×C32×C5
HallC32×#13133724 ⋊ C2
HallC32×C11×D31 ⋊ C5
Hall#13133724 ⋊ C2×C32
HallC11×D31 ⋊ C32×C5
HallC32×D31 ⋊ C11⋊C5
HallC32×C31 ⋊ C2×C11⋊C5
HallC32×C11 ⋊ D31⋊C5
HallD31 ⋊ C32×C11⋊C5
SylowC31 ⋊ C2×C32×C11⋊C5
SylowC11 ⋊ C32×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC32#16811774
commutator, cosocle, hypocenterC11×C31C2×C32×C5
FrattiniC1G
Fitting, socleC32×C11×C31C2×C5
LCSG ▷ C11×C31
UCSC1 ◁ C32

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3069

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 158);