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C5×Dic7×C169 #37556773

order23660
automorphism?
homologyAbelianization (H1) = C4×C5×C169 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic7×C169
unambiguous semidirect productC7⋊(C4×C5×C169)

Splittings

derived, SylowC7 ⋊ C4×C5×C169
HallC5×C7×C169 ⋊ C4
HallC7×C169 ⋊ C4×C5
HallC5×C7 ⋊ C4×C169

Subgroups

subgroupG/H
center, hypercenterC2×C5×C169D7
commutator, hypocenterC7C4×C5×C169
FrattiniC2×C13C5×C13×D7
FittingC2×C5×C7×C169C2
socle, prime radicalC2×C5×C7×C13C2×C13
cosocleC2×C7×C13C2×C5×C13
LCSG ▷ C7
UCSC1 ◁ C2×C5×C169

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23660

Conjugacy classes & character table

8450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23660, 3);