Finite Group Databasebeta

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C4×C7⋊C9×C113 #43249752

order28476
automorphism?
homologyAbelianization (H1) = C4×C9×C113 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7⋊C9×C113
unambiguous semidirect product(C4×C7)⋊(C9×C113)
unambiguous semidirect product(C4×C7×C113)⋊C9

Splittings

derived, SylowC7 ⋊ C4×C9×C113
HallC4×C7×C113 ⋊ C9
HallC7×C113 ⋊ C4×C9
HallC4×C7 ⋊ C9×C113

Subgroups

subgroupG/H
center, hypercenterC3×C4×C113ΓL(1,𝔽8)
commutator, hypocenterC7C4×C9×C113
FrattiniC2×C3C2×ΓL(1,𝔽8)×C113
FittingC3×C4×C7×C113C3
socle, prime radicalC2×C3×C7×C113C2×C3
cosocleC2×C3×C7C2×C3×C113
LCSG ▷ C7
UCSC1 ◁ C3×C4×C113

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28476

Conjugacy classes & character table

6780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28476, 3);