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C2×C5⋊D5×C169 #30683373

order16900
isoclinismisoclinic class of C5⋊D5
automorphism?
homologyAbelianization (H1) = C22×C169 · Schur multiplier (H2) = C2×C5

Aliases

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

Splittings

FittingC2×C52×C169 ⋊ C2
derived, SylowC52 ⋊ C22×C169
HallC52×C169 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C169C5⋊D5
commutator, hypocenterC52C22×C169
FrattiniC13C2×C13×C5⋊D5
FittingC2×C52×C169C2
socleC2×C52×C13C2×C13
prime radicalC2×C13×C5⋊D5C13
cosocleC52×C13C22×C13
LCSG ▷ C52
UCSC1 ◁ C2×C169

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8450

Conjugacy classes & character table

4732 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16900, 49);