Finite Group Databasebeta

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C4×C5×C112⋊C9 #36344809

order21780
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C11

Aliases

direct productC4×C5×C112⋊C9
unambiguous semidirect product(C4×C5×C112)⋊C9

Splittings

derived, SylowC112 ⋊ C4×C5×C9
HallC4×C5×C112 ⋊ C9
HallC5×C112 ⋊ C4×C9
HallC4×C112 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5C112⋊C3
commutator, hypocenterC112C4×C5×C9
FrattiniC2×C3C2×C5×C112⋊C3
FittingC3×C4×C5×C112C3
socle, prime radicalC2×C3×C5×C112C2×C3
cosocleC2×C3×C112C2×C3×C5
LCSG ▷ C112
UCSC1 ◁ C3×C4×C5

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2580 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 158);