Finite Group Databasebeta

← Prev (#11764092) Next (#11764094) →

AGL(1,𝔽5)×C11⋊C5 #11764093

order1100
isoclinismisoclinic class of AGL(1,𝔽5)×C11⋊C5
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×C11⋊C5
unambiguous semidirect product(C11×AGL(1,𝔽5))⋊C5

Splittings

Fitting, socle, derivedC5×C11 ⋊ C4×C5
HallC5×C11⋊C5 ⋊ C4
SylowC11 ⋊ C5×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C11C4×C5
prime radicalD5×C11⋊C5C2
cosocleD5×C11C2×C5
LCSG ▷ C5×C11
UCSC1

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 55

Conjugacy classes & character table

35 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽5)×C11⋊C5, C11⋊C5×ΓL(1,𝔽16), AGL(1,𝔽5)×C121⋊C5, …
maximal normal subgroup ofC3×AGL(1,𝔽5)×C11⋊C5, C11×AGL(1,𝔽5)×C11⋊C5, C13×AGL(1,𝔽5)×C11⋊C5, …
maximal quotient ofC3×AGL(1,𝔽5)×C11⋊C5, C11⋊C5×ΓL(1,𝔽16), AGL(1,𝔽5)×C121⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1100, 26);