Finite Group Databasebeta

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C3×#11716101 #72246602

order2352
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productC3×#11716101

Splittings

HallC3×C72 ⋊ C2×Q8
SylowC72 ⋊ C2×C3×Q8

Subgroups

subgroupG/H
centerC2×C3C2×D72
commutator, cosocleC2×C72C23×C3
FrattiniC2C2×C3×D72
FittingC3×C4×C72C22
socleC2×C3×C72C23
prime radicalC2×C3×C7⋊D7C22
hypercenterC3×C4D72
hypocenterC72C2×C3×Q8
LCSG ▷ C2×C72 ▷ C72
UCSC1 ◁ C2×C3 ◁ C3×C4

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#11716101, C3×#13096694, #72246661, …
maximal normal subgroup ofD3×#11716101, C3×#13096694, #72246661, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.