Finite Group Databasebeta

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C2×C3×#67×#1043 #72259599

order14400
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×C3×#67×#1043

Splittings

FittingC23×C32×C52 ⋊ C2×C4
HallC32×C52 ⋊ C2×C4×D4
SylowC52 ⋊ C2×C3×C4×#67
SylowC32 ⋊ C2×D4×#1043

Subgroups

subgroupG/H
centerC22×C3C2×D3×#1043
commutatorC2×C3×C52C23×C3×C4
FrattiniC2C22×C3×D3×#1043
FittingC23×C32×C52C2×C4
socleC22×C32×C52C22×C4
prime radicalC2×C3×#67×C5⋊D5C2
cosocleC2×C3×C5⋊D5C24×C3
hypercenterC23×C3D3×#1043
hypocenterC3×C52C2×C3×C4×D4
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C22×C3 ◁ C23×C3

7760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 600

Conjugacy classes & character table

540 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×#1043×#3811
maximal normal subgroup ofC2×#1043×#3811

GAP

Past the SmallGroups library coverage — no SmallGroups id.