Finite Group Databasebeta

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C3×D5×D77 #17987690

order4620
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×D77
unambiguous semidirect product(D5×C11)⋊(C3×D7)

Splittings

Fitting, socle, HallC3×C5×C7×C11 ⋊ C22
derived, HallC5×C7×C11 ⋊ C22×C3
HallC3×C7×C11 ⋊ C2×D5
HallC3×C5×C11 ⋊ C2×D7
HallC3×C5×C7 ⋊ C2×D11
HallC7×C11 ⋊ C2×C3×D5
HallC5×C11 ⋊ C2×C3×D7
HallC5×C7 ⋊ C2×C3×D11
HallC3×C11 ⋊ D5×D7
HallC3×C7 ⋊ D5×D11
HallC3×C5 ⋊ C2×D77
SylowC11 ⋊ C3×D5×D7
SylowC7 ⋊ C3×D5×D11
SylowC5 ⋊ C2×C3×D77

Subgroups

subgroupG/H
center, hypercenterC3D5×D77
commutator, cosocle, hypocenterC5×C7×C11C22×C3
FrattiniC1G
Fitting, socleC3×C5×C7×C11C22
LCSG ▷ C5×C7×C11
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD5×C11⋊(D7⋊C9), C9×D5×D77, C3×D5×C11⋊AGL(1,𝔽7), …
maximal normal subgroup ofD5×C11⋊(D7⋊C9), C9×D5×D77, C3×D5×C11⋊AGL(1,𝔽7), …
maximal quotient ofC9×D5×D77, C32×D5×D77, C3×D15×D77, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4620, 87);