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C7×Dic9×C113 #43249756

order28476
automorphism?
homologyAbelianization (H1) = C4×C7×C113 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic9×C113
unambiguous semidirect productC9⋊(C4×C7×C113)

Splittings

derived, SylowC9 ⋊ C4×C7×C113
HallC7×C9×C113 ⋊ C4
HallC9×C113 ⋊ C4×C7
HallC7×C9 ⋊ C4×C113

Subgroups

subgroupG/H
center, hypercenterC2×C7×C113D9
commutator, hypocenterC9C4×C7×C113
FrattiniC2×C3D3×C7×C113
FittingC2×C7×C9×C113C2
socle, prime radicalC2×C3×C7×C113D3
cosocleC2×C9C2×C7×C113
LCSG ▷ C9
UCSC1 ◁ C2×C7×C113

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28476

Conjugacy classes & character table

9492 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28476, 7);