Finite Group Databasebeta

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C3×C4×C5×#10597243 #49137301

order36300
automorphism?
homologyAbelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC3×C4×C5×#10597243

Splittings

FittingC3×C4×C5×C112 ⋊ C5
derived, SylowC112 ⋊ C3×C4×C52
HallC3×C4×C112 ⋊ C52
HallC4×C112 ⋊ C3×C52
HallC3×C112 ⋊ C4×C52

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5#10597243
commutator, hypocenterC112C3×C4×C52
FrattiniC2C2×C3×C5×#10597243
FittingC3×C4×C5×C112C5
socleC2×C3×C5×C112C2×C5
prime radicalC2×C3×C5×#10597243C2
cosocleC2×C112C2×C3×C52
LCSG ▷ C112
UCSC1 ◁ C3×C4×C5

672 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7260

Conjugacy classes & character table

1740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 437);