Finite Group Databasebeta

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Cayley diagram

C2×D100 #87743

order400
isoclinismisoclinic class of Dic50
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC2×D100

Splittings

FittingC2×C4×C25 ⋊ C2
SylowC25 ⋊ C2×D4

Subgroups

subgroupG/H
centerC22C2×D25
commutator, cosocleC2×C25C23
FrattiniC2×C5C22×D5
FittingC2×C4×C25C2
socleC22×C5C2×D5
hypercenterC2×C4D25
hypocenterC25C2×D4
LCSG ▷ C2×C25 ▷ C25
UCSC1 ◁ C22 ◁ C2×C4

81 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 200

A minimal faithful permutation representation — 3 generators on 31 points:

(3,4,5,6)(7,27,18,30,15,13,20,11,29,10,22,12,28,24,19,14,8,31,16,26,9,21,25,17,23);(1,2)(4,6)(8,10)(9,13)(11,16)(12,19)(14,22)(15,21)(17,18)(20,26)(23,27)(24,28)(25,30)(29,31);(1,2)

Conjugacy classes & character table

106 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11716358, #11716369, #11716372, …
maximal normal subgroup of#11716358, #11716369, #11716372, …
maximal quotient of#11716431, C4×D100, #11716436, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 37);