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C5×Dic3×C169 #23778351

order10140
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C4×C5×C169 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic3×C169
unambiguous semidirect productC3⋊(C4×C5×C169)

Splittings

derived, SylowC3 ⋊ C4×C5×C169
HallC3×C5×C169 ⋊ C4
HallC3×C169 ⋊ C4×C5
HallC3×C5 ⋊ C4×C169

Subgroups

subgroupG/H
center, hypercenterC2×C5×C169D3
commutator, hypocenterC3C4×C5×C169
FrattiniC2×C13C5×D3×C13
FittingC2×C3×C5×C169C2
socle, prime radicalC2×C3×C5×C13C2×C13
cosocleC2×C3×C13C2×C5×C13
LCSG ▷ C3
UCSC1 ◁ C2×C5×C169

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5070 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×Dic9×C169, C5×Dic3×C169⋊C3, C3×C5×Dic3×C169, …
maximal normal subgroup ofC5×Dic3×C169⋊C3, C3×C5×Dic3×C169
maximal quotient ofC5×Dic9×C169, C3×C5×Dic3×C169, C5×C3⋊Dic3×C169

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 9);