Finite Group Databasebeta

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Cayley diagram

C3×#3792 #88986

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

Aliases

direct productC3×#3792

Splittings

SylowC33 ⋊ M16

Subgroups

subgroupG/H
centerC2×C3C2×#157
commutatorC2×C32C2×C3×C4
FrattiniC2C2×C3×#157
Fitting, prime radicalC22×C33C4
socleC2×C33C2×C4
cosocleC3⋊Dic3C22×C3
hypercenterC22×C3#157
hypocenterC32C3×M16
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C22×C3

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 17
transitive degreeμt(G) = 24

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

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

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11722729, #11722730, C3×#63741, …
maximal normal subgroup of#11722729, #11722730, C3×#63741, …
maximal quotient ofC3×#63777, C3×#63779, C3×C22⋊#622, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 633);