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3−1+2×C79⋊C9 #34063246

order19197
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C32

Aliases

direct product3−1+2×C79⋊C9

Splittings

SylowC79 ⋊ C9×3−1+2

Subgroups

subgroupG/H
center, FrattiniC32C32×C79⋊C3
commutatorC3×C79C32×C9
FittingC3×3−1+2×C79C3
socle, cosocleC32×C79C33
prime radicalC33×C79C32
hypercenterC3×3−1+2C79⋊C3
hypocenterC79C9×3−1+2
LCSG ▷ C3×C79 ▷ C79
UCSC1 ◁ C32 ◁ C3×3−1+2

148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6399

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19197, 175);