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C4×#19104441 #35208783

order20748
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC4×#19104441

Splittings

Fitting, HallC4×C7×C13×C19 ⋊ C3
derived, HallC7×C13×C19 ⋊ C3×C4
HallC4×C13×C19 ⋊ ΓL(1,𝔽8)
HallC4×C7×C19 ⋊ C13⋊C3
HallC4×C7×C13 ⋊ C19⋊C3
HallC13×C19 ⋊ C4×ΓL(1,𝔽8)
HallC7×C19 ⋊ C4×C13⋊C3
HallC7×C13 ⋊ C4×C19⋊C3
HallC4×C19 ⋊ #63270
HallC4×C13 ⋊ #87705
HallC4×C7 ⋊ #10625203
SylowC19 ⋊ C4×#63270
SylowC13 ⋊ C4×#87705
SylowC7 ⋊ C4×#10625203

Subgroups

subgroupG/H
center, hypercenterC4#19104441
commutator, hypocenterC7×C13×C19C3×C4
FrattiniC2C2×#19104441
FittingC4×C7×C13×C19C3
socle, cosocleC2×C7×C13×C19C2×C3
prime radicalC2×#19104441C2
LCSG ▷ C7×C13×C19
UCSC1 ◁ C4

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6916

Conjugacy classes & character table

2316 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 11);