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C22×C41⋊C5 #11717958

order820
isoclinismisoclinic class of C41⋊C5
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC22×C41⋊C5
unambiguous semidirect product(C22×C41)⋊C5

Splittings

Fitting, socle, HallC22×C41 ⋊ C5
derived, SylowC41 ⋊ C22×C5

Subgroups

subgroupG/H
center, hypercenterC22C41⋊C5
commutator, cosocle, hypocenterC41C22×C5
FrattiniC1G
Fitting, socleC22×C41C5
LCSG ▷ C41
UCSC1 ◁ C22

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 164

A minimal faithful permutation representation — 2 generators on 45 points:

(1,2)(6,7,9,13,21)(8,11,17,28,39)(10,15,24,16,26)(12,19,27,38,25)(14,23,34,22,33)(18,29,40,44,37)(20,32,31,42,45)(30,41,35,43,36);(3,4)(5,6,8,12,20,29,33,38,44,40,7,10,16,27,34,41,13,22,9,14,11,18,30,42,43,45,23,35,15,25,19,31,28,39,24,36,17,21,26,37,32)

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×Dic41⋊C5, C22⋊(D41⋊C5), C2×C4×C41⋊C5, …
maximal normal subgroup ofC2×Dic41⋊C5, C22⋊(D41⋊C5), C2×C4×C41⋊C5, …
maximal quotient ofC2×C4×C41⋊C5, D4×C41⋊C5, Q8×C41⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(820, 9);