Finite Group Databasebeta

← Prev (#11925326) Next (#11925328) →

C3×#87829 #11925327

order1200
isoclinismisoclinic class of (C2×AGL(1,𝔽5))⋊D5
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×#87829

Splittings

HallC3×C52 ⋊ M16
SylowC52 ⋊ C3×M16

Subgroups

subgroupG/H
center, hypercenterC2×C3D5×AGL(1,𝔽5)
commutatorC2×C52C2×C3×C4
FrattiniC2C3×D5×AGL(1,𝔽5)
Fitting, socleC2×C3×C52C2×C4
prime radicalC2×C3×C5⋊D5C4
cosocleC5×Dic5C22×C3
hypocenterC52C3×M16
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C3

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 120

A minimal faithful permutation representation — 2 generators on 21 points:

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

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#11717347, D3×#87829, #72231067, …
maximal normal subgroup ofC3×#11717347, D3×#87829, #72231067
maximal quotient ofC3×#11925377

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 537);