Finite Group Databasebeta

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C3×C22⋊#1044 #11925512

order1200
isoclinismisoclinic class of #87863
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22×C5

Aliases

direct productC3×C22⋊#1044

Splittings

FittingC22×C3×C52 ⋊ C4
HallC3×C52 ⋊ C22⋊C4
SylowC52 ⋊ C3×C22⋊C4

Subgroups

subgroupG/H
centerC2×C3C2×#1044
commutatorC2×C52C2×C3×C4
FrattiniC2C2×C3×#1044
FittingC22×C3×C52C4
socleC2×C3×C52C2×C4
prime radicalC22×C3×C5⋊D5C2
cosocleC2×C5⋊D5C22×C3
hypercenterC22×C3#1044
hypocenterC52C3×C22⋊C4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C3 ◁ C22×C3

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 17
transitive degreeμt(G) = 60

A minimal faithful permutation representation — 2 generators on 17 points:

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

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#11717375, D3×C22⋊#1044, #72224581, …
maximal normal subgroup ofC3×#11717375, D3×C22⋊#1044, #72224581, …
maximal quotient ofC3×#11925540, C32×C22⋊#1044, C2×C3×C22⋊#1044, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 722);