Finite Group Databasebeta

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C3×C4×C7×C112⋊C3 #44479033

order30492
automorphism?
homologyAbelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3×C11

Aliases

direct productC3×C4×C7×C112⋊C3
unambiguous semidirect product(C4×C112)⋊(C32×C7)
unambiguous semidirect product(C3×C4×C112)⋊(C3×C7)

Splittings

FittingC3×C4×C7×C112 ⋊ C3
derived, SylowC112 ⋊ C32×C4×C7
HallC4×C7×C112 ⋊ C32
HallC7×C112 ⋊ C32×C4
HallC4×C112 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC3×C4×C7C112⋊C3
commutator, hypocenterC112C32×C4×C7
FrattiniC2C2×C3×C7×C112⋊C3
FittingC3×C4×C7×C112C3
socleC2×C3×C7×C112C2×C3
prime radicalC2×C3×C7×C112⋊C3C2
cosocleC2×C112C2×C32×C7
LCSG ▷ C112
UCSC1 ◁ C3×C4×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Conjugacy classes & character table

3612 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 256);