Finite Group Databasebeta

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Cayley diagram

C4×#1035 #87736

order400
isoclinismisoclinic class of #1035
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C4

Aliases

direct productC4×#1035

Splittings

FittingC4×C25 ⋊ C4
derived, SylowC25 ⋊ C42

Subgroups

subgroupG/H
center, hypercenterC4#1035
commutator, hypocenterC25C42
Frattini, socleC2×C5C2×AGL(1,𝔽5)
FittingC4×C25C4
prime radical, cosocleC2×D25C22
LCSG ▷ C25
UCSC1 ◁ C4

45 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 29 points:

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

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC8×#1035, #11716410, #11716423, …
maximal normal subgroup ofC8×#1035, #11716410, #11716423, …
maximal quotient ofC8×#1035, #11716410, C4×#6016, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 30);