Finite Group Databasebeta

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C11×D5⋊AGL(1,𝔽5) #72228512

order2200
isoclinismisoclinic class of D5⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D5⋊AGL(1,𝔽5)

Splittings

Fitting, socle, HallC52×C11 ⋊ C2×C4
derived, SylowC52 ⋊ C2×C4×C11

Subgroups

subgroupG/H
center, hypercenterC11D5⋊AGL(1,𝔽5)
commutator, hypocenterC52C2×C4×C11
FrattiniC1G
Fitting, socleC52×C11C2×C4
prime radicalD52×C11C2
cosocleC5⋊D5C22×C11
LCSG ▷ C52
UCSC1 ◁ C11

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 110

A minimal faithful permutation representation — 2 generators on 21 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,14,19,18)(13,15,17,16);(12,17,20,21,19,13,14,16,18,15)

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11⋊C5×D5⋊AGL(1,𝔽5), D11×D5⋊AGL(1,𝔽5), C11×AGL(1,𝔽5)2, …
maximal normal subgroup ofC11⋊C5×D5⋊AGL(1,𝔽5), D11×D5⋊AGL(1,𝔽5), C11×AGL(1,𝔽5)2, …

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2,3,4,5,6,7,8,9,10,11)(12,14,19,18)(13,15,17,16), (12,17,20,21,19,13,14,16,18,15));