Finite Group Databasebeta

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C5×C22⋊C9×C169 #44477455

order30420
automorphism?
homologyAbelianization (H1) = C5×C9×C169 · Schur multiplier (H2) = C2

Aliases

direct productC5×C22⋊C9×C169
unambiguous semidirect productC22⋊(C5×C9×C169)
unambiguous semidirect product(C22×C5)⋊(C9×C169)

Splittings

derived, SylowC22 ⋊ C5×C9×C169
HallC22×C5×C169 ⋊ C9
HallC22×C169 ⋊ C5×C9
HallC22×C5 ⋊ C9×C169

Subgroups

subgroupG/H
center, hypercenterC3×C5×C169A4
commutator, hypocenterC22C5×C9×C169
FrattiniC3×C13C5×A4×C13
FittingC22×C3×C5×C169C3
socle, prime radicalC22×C3×C5×C13C3×C13
cosocleC22×C3×C13C3×C5×C13
LCSG ▷ C22
UCSC1 ◁ C3×C5×C169

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15210

Conjugacy classes & character table

10140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 44);