Finite Group Databasebeta

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C2×D45×C169 #44477462

order30420
automorphism?
homologyAbelianization (H1) = C22×C169 · Schur multiplier (H2) = C2

Aliases

direct productC2×D45×C169
unambiguous semidirect product(C2×C5)⋊(D9×C169)
unambiguous semidirect product(C2×C9)⋊(D5×C169)

Splittings

FittingC2×C5×C9×C169 ⋊ C2
derived, HallC5×C9 ⋊ C22×C169
HallC5×C9×C169 ⋊ C22
HallC9×C169 ⋊ C2×D5
HallC5×C169 ⋊ C2×D9
SylowC9 ⋊ C2×D5×C169
SylowC5 ⋊ C2×D9×C169

Subgroups

subgroupG/H
center, hypercenterC2×C169D45
commutator, hypocenterC5×C9C22×C169
FrattiniC3×C13C2×C13×D15
FittingC2×C5×C9×C169C2
socleC2×C3×C5×C13D3×C13
prime radicalC2×C13×D45C13
cosocleC5×C9×C13C22×C13
LCSG ▷ C5×C9
UCSC1 ◁ C2×C169

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15210

Conjugacy classes & character table

8112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 51);