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D77⋊D15 #17987707

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

Aliases

unambiguous semidirect productD77⋊D15

Splittings

Fitting, socle, derived, HallC3×C5×C7×C11 ⋊ C22
HallC5×C7×C11 ⋊ C2×D3
HallC3×C7×C11 ⋊ C2×D5
HallC3×C5×C11 ⋊ C2×D7
HallC3×C5×C7 ⋊ C2×D11
HallC7×C11 ⋊ C2×D15
HallC5×C11 ⋊ D3×D7
HallC5×C7 ⋊ D3×D11
HallC3×C11 ⋊ D5×D7
HallC3×C7 ⋊ D5×D11
HallC3×C5 ⋊ D7×D11
SylowC11 ⋊ D7×D15
SylowC7 ⋊ D11×D15
SylowC5 ⋊ D21⋊D11
SylowC3 ⋊ D35⋊D11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C7×C11C22
LCSG ▷ C3×C5×C7×C11
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

Polycyclic presentation:

2^2,3,5,7,11|e^a=e^6,f^a=f^10,c^b=c^2,d^b=d^4,e^b=e^6

Conjugacy classes & character table

315 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD77⋊D45, (C11⋊AGL(1,𝔽7))⋊D15, C3×D77⋊D15, …
maximal normal subgroup of(C11⋊AGL(1,𝔽7))⋊D15, C3×D77⋊D15, (C7⋊AGL(1,𝔽11))⋊D15, …
maximal quotient ofD77⋊D45, C3×D77⋊D15, D77⋊(C3⋊D15), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4620, 104);