Finite Group Databasebeta

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C2×C3×#11925540 #72230743

order7200
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24×C5

Aliases

direct productC2×C3×#11925540

Splittings

FittingC23×C32×C52 ⋊ C4
HallC32×C52 ⋊ C2×C22⋊C4
SylowC52 ⋊ C2×C3×#217
SylowC32 ⋊ C2×C22⋊#1044

Subgroups

subgroupG/H
centerC22×C3C2×C3⋊#1044
commutatorC2×C3×C52C22×C3×C4
FrattiniC2C22×C3×C3⋊#1044
FittingC23×C32×C52C4
socleC22×C32×C52C2×C4
prime radicalC23×C32×C5⋊D5C2
cosocleC2×C3×C5⋊D5C23×C3
hypercenterC23×C3C3⋊#1044
hypocenterC3×C52C2×C3×C22⋊C4
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C22×C3 ◁ C23×C3

2128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C3×#72224585
maximal normal subgroup ofC2×C3×#72224585

GAP

Past the SmallGroups library coverage — no SmallGroups id.