Finite Group Databasebeta

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C3×#13107767 #72259805

order4800
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25×C5

Aliases

direct productC3×#13107767

Splittings

FittingC2×C3×C52×D4 ⋊ C4
HallC3×C52 ⋊ #518
SylowC52 ⋊ C3×#518

Subgroups

subgroupG/H
centerC2×C3C23×#1044
commutatorC2×C52C23×C3×C4
FrattiniC2C23×C3×#1044
FittingC2×C3×C52×D4C4
socleC2×C3×C52C23×C4
prime radicalC2×C3×D4×C5⋊D5C2
cosocleC2×C5⋊D5C24×C3
hypercenterC2×C3×D4#1044
hypocenterC52C3×#518
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C3 ◁ C2×C3×D4

1824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×#72213412
maximal normal subgroup ofC3×#72213412

GAP

Past the SmallGroups library coverage — no SmallGroups id.