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Cayley diagram

C22×#1035 #87759

order400
isoclinismisoclinic class of #1035
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC22×#1035
unambiguous semidirect productD25⋊(C2×C4)

Splittings

FittingC22×C25 ⋊ C4
derived, SylowC25 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC22#1035
commutator, hypocenterC25C22×C4
FrattiniC5C22×AGL(1,𝔽5)
FittingC22×C25C4
socleC22×C5AGL(1,𝔽5)
prime radicalC22×D25C2
cosocleD25C23
LCSG ▷ C25
UCSC1 ◁ C22

81 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 100

A minimal faithful permutation representation — 3 generators on 29 points:

(6,8,9,14)(7,12,13,24)(10,18,19,23)(11,21,22,15)(16,26,27,29)(17,20,25,28);(3,4)(5,6,10,20,17,7,11,8,15,26,12,23,16,27,18,24,29,21,14,22,13,25,28,19,9);(1,2)

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×#1035)⋊C4, C2×C4×#1035, C2×C4⋊#1035, …
maximal normal subgroup of(C2×#1035)⋊C4, C2×C4×#1035, C2×C4⋊#1035, …
maximal quotient ofC2×D25⋊C8, C2×#87735, D25⋊M16, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 53);