Finite Group Databasebeta

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Cayley diagram

C8×C3⋊Dic3 #63640

order288
isoclinismisoclinic class of C3⋊D3
automorphism?
homologyAbelianization (H1) = C4×C8 · Schur multiplier (H2) = C3×C4

Aliases

direct productC8×C3⋊Dic3

Splittings

derived, SylowC32 ⋊ C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C8C3⋊D3
commutator, hypocenterC32C4×C8
FrattiniC2×C4C2×C3⋊D3
FittingC2×C32×C8C2
socle, prime radicalC22×C32C2×C4
cosocleC2×C32×C4C22
LCSG ▷ C32
UCSC1 ◁ C2×C8

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 288

A minimal faithful permutation representation — 3 generators on 18 points:

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

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10589102, #10589104, #10589133, …
maximal normal subgroup of#10589102, #10589104, #10589133, …
maximal quotient ofC8×C3⋊(C3⋊C8), #10589320, C16×C3⋊Dic3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 288);