Finite Group Databasebeta

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C3×C22⋊C4×#1043 #72260145

order4800
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC3×C22⋊C4×#1043

Splittings

FittingC3×C52×C22⋊C4 ⋊ C4
HallC3×C52 ⋊ C4×C22⋊C4
SylowC52 ⋊ C3×C4×C22⋊C4

Subgroups

subgroupG/H
centerC22×C3C22×#1043
commutatorC2×C52C2×C3×C42
FrattiniC22C22×C3×#1043
FittingC3×C52×C22⋊C4C4
socleC22×C3×C52C22×C4
prime radicalC23×C3×C5⋊D5C22
cosocleC22×C5⋊D5C23×C3
hypercenterC3×C22⋊C4#1043
hypocenterC52C3×C4×C22⋊C4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22×C3 ◁ C3×C22⋊C4

2064 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 600

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×C22⋊C4×#1043
maximal normal subgroup ofD3×C22⋊C4×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.