Finite Group Databasebeta

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Cayley diagram

C22×#1042 #87921

order400
isoclinismisoclinic class of #1042
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC22×#1042
unambiguous semidirect productD5⋊(C2×Dic5)

Splittings

Fitting, socleC22×C52 ⋊ C4
derived, SylowC52 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC22#1042
commutator, hypocenterC52C22×C4
FrattiniC1G
Fitting, socleC22×C52C4
prime radicalC22×C5×D5C2
cosocleC5×D5C23
LCSG ▷ C52
UCSC1 ◁ C22

113 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 14
transitive degreeμt(G) = 80

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

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×AGL(1,𝔽5))⋊Dic5, #11716849, C2×Dic5×AGL(1,𝔽5), …
maximal normal subgroup of(C2×AGL(1,𝔽5))⋊Dic5, #11716849, C2×Dic5×AGL(1,𝔽5), …
maximal quotient ofC2×D5⋊#168, C2×#87849, D5⋊#681, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 215);