Finite Group Databasebeta

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Cayley diagram

C4×D52 #87875

order400
isoclinismisoclinic class of D52
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×D52

Splittings

FittingC4×C52 ⋊ C22
derived, SylowC52 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC4D52
commutator, hypocenterC52C22×C4
FrattiniC2C2×D52
FittingC4×C52C22
socle, cosocleC2×C52C23
prime radicalC2×D52C2
LCSG ▷ C52
UCSC1 ◁ C4

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 14
transitive degreeμt(G) = 40

A minimal faithful permutation representation — 3 generators on 14 points:

(5,6,8,9,7)(11,12)(13,14);(6,7)(8,9)(10,11,13,14,12);(1,2,3,4)

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11716784, C8×D52, D5×#676, …
maximal normal subgroup of#11716784, C8×D52, D5×#676, …
maximal quotient ofC8×D52, D5×#676, #11716909, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 169);