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C22×C49×ΓL(1,𝔽32) #44477109

order30380
automorphism?
homologyAbelianization (H1) = C22×C5×C49 · Schur multiplier (H2) = C2

Aliases

direct productC22×C49×ΓL(1,𝔽32)
unambiguous semidirect product(C22×C31)⋊(C5×C49)
unambiguous semidirect product(C22×C31×C49)⋊C5

Splittings

Fitting, HallC22×C31×C49 ⋊ C5
derived, SylowC31 ⋊ C22×C5×C49
HallC31×C49 ⋊ C22×C5
HallC22×C31 ⋊ C5×C49

Subgroups

subgroupG/H
center, hypercenterC22×C49ΓL(1,𝔽32)
commutator, hypocenterC31C22×C5×C49
FrattiniC7C22×C7×ΓL(1,𝔽32)
FittingC22×C31×C49C5
socleC22×C7×C31C5×C7
prime radicalC22×C7×ΓL(1,𝔽32)C7
cosocleC7×C31C22×C5×C7
LCSG ▷ C31
UCSC1 ◁ C22×C49

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6076

Conjugacy classes & character table

2156 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30380, 18);