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C5⋊D385 #16838693

order3850
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C5

Aliases

unambiguous semidirect productC5⋊D385
unambiguous semidirect productC7⋊(C5⋊D55)
unambiguous semidirect productC11⋊(C5⋊D35)

Splittings

Fitting, socle, derived, HallC52×C7×C11 ⋊ C2
HallC52×C11 ⋊ D7
HallC52×C7 ⋊ D11
HallC7×C11 ⋊ C5⋊D5
SylowC52 ⋊ D77
SylowC11 ⋊ C5⋊D35
SylowC7 ⋊ C5⋊D55

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C7×C11C2
LCSG ▷ C52×C7×C11
UCSC1

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1925

Polycyclic presentation:

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

Conjugacy classes & character table

964 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5⋊(C5⋊(C11⋊AGL(1,𝔽7))), C11⋊#11760386, C11⋊#11760384, …
maximal normal subgroup ofC5⋊(C5⋊(C11⋊AGL(1,𝔽7))), C11⋊#11760386, C11⋊#11760384, …
maximal quotient ofC3⋊(C5⋊D385), C3×C5⋊D385, C5⋊D2695, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3850, 32);