Finite Group Databasebeta

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Cayley diagram

C2×#6014 #87715

order400
isoclinismisoclinic class of D25
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C2

Aliases

direct productC2×#6014

Splittings

derived, SylowC25 ⋊ C2×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4D25
commutator, hypocenterC25C2×C8
FrattiniC4×C5C2×D5
FittingC2×C4×C25C2
socle, prime radicalC22×C5Dic5
cosocleC4×C25C22
LCSG ▷ C25
UCSC1 ◁ C2×C4

33 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 400

A minimal faithful permutation representation — 2 generators on 35 points:

(1,2)(3,4,5,7,6,8,9,10)(12,14)(13,17)(15,20)(16,23)(18,26)(19,25)(21,22)(24,30)(27,31)(28,32)(29,34)(33,35);(1,2)(11,25,35,28,14,17,31,29,20,23,26,24,22,21,30,18,16,15,34,27,13,12,32,33,19)

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#6014, #11716351, C4⋊#6014, …
maximal normal subgroup ofC4×#6014, #11716351, C4⋊#6014, …
maximal quotient ofC4×#6014, C4⋊#6014, C2×#87707, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 9);