Finite Group Databasebeta

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C4×C7×C112⋊C9 #44478903

order30492
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C11

Aliases

direct productC4×C7×C112⋊C9
unambiguous semidirect product(C4×C112)⋊(C7×C9)

Splittings

derived, SylowC112 ⋊ C4×C7×C9
HallC4×C7×C112 ⋊ C9
HallC7×C112 ⋊ C4×C9
HallC4×C112 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC3×C4×C7C112⋊C3
commutator, hypocenterC112C4×C7×C9
FrattiniC2×C3C2×C7×C112⋊C3
FittingC3×C4×C7×C112C3
socle, prime radicalC2×C3×C7×C112C2×C3
cosocleC2×C3×C112C2×C3×C7
LCSG ▷ C112
UCSC1 ◁ C3×C4×C7

84 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, 126);