Finite Group Databasebeta

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Cayley diagram

C3×C22⋊#157 #88987

order432
isoclinismisoclinic class of #3788
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22×C3

Aliases

direct productC3×C22⋊#157

Splittings

FittingC22×C33 ⋊ C4
SylowC33 ⋊ C22⋊C4

Subgroups

subgroupG/H
centerC2×C3C2×#157
commutatorC2×C32C2×C3×C4
FrattiniC2C2×C3×#157
FittingC22×C33C4
socleC2×C33C2×C4
prime radicalC22×C3×C3⋊D3C2
cosocleC2×C3⋊D3C22×C3
hypercenterC22×C3#157
hypocenterC32C3×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C22×C3

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 13
transitive degreeμt(G) = 24

A minimal faithful permutation representation — 2 generators on 13 points:

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

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11722727, #11722728, C3×#63738, …
maximal normal subgroup of#11722727, #11722728, C3×#63738, …
maximal quotient ofC3×#63774, C3×#63778, C3×#63780, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 634);