Finite Group Databasebeta

← Prev (#65712) Next (#65714) →

Cayley diagram

C2×D5⋊C16 #65713

order320
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×D5⋊C16
unambiguous semidirect productD5⋊(C2×C16)

Splittings

derived, SylowC5 ⋊ C22×C16

Subgroups

subgroupG/H
center, hypercenterC2×C8AGL(1,𝔽5)
commutator, hypocenterC5C22×C16
FrattiniC4C22×AGL(1,𝔽5)
FittingC2×C5×C8C4
socleC22×C5C2×C8
prime radicalC22×D5C8
cosocle#168C23
LCSG ▷ C5
UCSC1 ◁ C2×C8

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 160

A minimal faithful permutation representation — 3 generators on 23 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10598619, #10598620, #10598625, …
maximal normal subgroup of#10598619, #10598620, #10598625, …
maximal quotient ofC4×D5⋊C16, D5⋊(C4⋊C16), #10603828, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 1051);