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C2×C9×C191⋊C5 #31769893

order17190
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC2×C9×C191⋊C5
unambiguous semidirect product(C2×C191)⋊(C5×C9)
unambiguous semidirect product(C2×C9×C191)⋊C5

Splittings

Fitting, HallC2×C9×C191 ⋊ C5
derived, SylowC191 ⋊ C2×C5×C9
HallC9×C191 ⋊ C2×C5
HallC2×C191 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C9C191⋊C5
commutator, hypocenterC191C2×C5×C9
FrattiniC3C2×C3×C191⋊C5
FittingC2×C9×C191C5
socleC2×C3×C191C3×C5
prime radicalC2×C3×C191⋊C5C3
cosocleC3×C191C2×C3×C5
LCSG ▷ C191
UCSC1 ◁ C2×C9

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3438

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC4×C9×C191⋊C5, C9×Dic191⋊C5, Dic9×C191⋊C5, …
maximal normal subgroup ofC4×C9×C191⋊C5, C9×Dic191⋊C5, Dic9×C191⋊C5, …
maximal quotient ofC4×C9×C191⋊C5, C22×C9×C191⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17190, 2);