Finite Group Databasebeta

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Cayley diagram

C4×C3⋊(C3⋊Dic3) #88856

order432
isoclinismisoclinic class of C3⋊(C3⋊D3)
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C33×C4

Aliases

direct productC4×C3⋊(C3⋊Dic3)

Splittings

derived, SylowC33 ⋊ C42

Subgroups

subgroupG/H
center, hypercenterC2×C4C3⋊(C3⋊D3)
commutator, hypocenterC33C42
FrattiniC22C2×C3⋊(C3⋊D3)
FittingC2×C33×C4C2
socle, prime radical, cosocleC22×C33C22
LCSG ▷ C33
UCSC1 ◁ C2×C4

420 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 17
transitive degreeμt(G) = 432

A minimal faithful permutation representation — 4 generators on 17 points:

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11722018, #11722021, #11722043, …
maximal normal subgroup of#11722018, #11722021, #11722043, …
maximal quotient ofC4×C3⋊(C3⋊(C3⋊C8)), #11722173, C8×C3⋊(C3⋊Dic3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 503);