Finite Group Databasebeta

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C7×D5×D33 #17987709

order4620
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D5×D33
unambiguous semidirect product(C3×D5)⋊(C7×D11)
unambiguous semidirect product(D5×C11)⋊(D3×C7)

Splittings

Fitting, socle, HallC3×C5×C7×C11 ⋊ C22
derived, HallC3×C5×C11 ⋊ C22×C7
HallC5×C7×C11 ⋊ C2×D3
HallC3×C7×C11 ⋊ C2×D5
HallC3×C5×C7 ⋊ C2×D11
HallC7×C11 ⋊ D3×D5
HallC5×C11 ⋊ C2×D3×C7
HallC5×C7 ⋊ C2×D33
HallC3×C11 ⋊ C2×C7×D5
HallC3×C7 ⋊ D5×D11
HallC3×C5 ⋊ C2×C7×D11
SylowC11 ⋊ D3×C7×D5
SylowC5 ⋊ C2×C7×D33
SylowC3 ⋊ C7×D5×D11

Subgroups

subgroupG/H
center, hypercenterC7D5×D33
commutator, cosocle, hypocenterC3×C5×C11C22×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C11C22
LCSG ▷ C3×C5×C11
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 1155

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×D5×D99, D5×ΓL(1,𝔽8)×D33, C3×C7×D5×D33, …
maximal normal subgroup ofD5×ΓL(1,𝔽8)×D33, C3×C7×D5×D33, C7×D5×C3⋊AGL(1,𝔽11), …
maximal quotient ofC7×D5×D99, C3×C7×D5×D33, C7×D5×C3⋊D33, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4620, 106);