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C22×C5×#13095276 #44501458

order30660
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×#13095276

Splittings

Fitting, socle, HallC22×C5×C7×C73 ⋊ C3
derived, HallC7×C73 ⋊ C22×C3×C5
HallC5×C7×C73 ⋊ C22×C3
HallC22×C7×C73 ⋊ C3×C5
HallC22×C5×C73 ⋊ ΓL(1,𝔽8)
HallC5×C73 ⋊ C22×ΓL(1,𝔽8)
HallC22×C73 ⋊ C5×ΓL(1,𝔽8)
HallC22×C5×C7 ⋊ C73⋊C3
SylowC73 ⋊ C22×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C22×C73⋊C3
HallC22×C7 ⋊ C5×C73⋊C3
SylowC7 ⋊ C22×C5×C73⋊C3

Subgroups

subgroupG/H
center, hypercenterC22×C5#13095276
commutator, cosocle, hypocenterC7×C73C22×C3×C5
FrattiniC1G
Fitting, socleC22×C5×C7×C73C3
LCSG ▷ C7×C73
UCSC1 ◁ C22×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10220

Conjugacy classes & character table

3460 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 221);