Finite Group Databasebeta

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C5×C7×#10621721 #37556780

order23660
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×#10621721

Splittings

Fitting, HallC5×C7×C169 ⋊ C4
derived, SylowC169 ⋊ C4×C5×C7
HallC7×C169 ⋊ C4×C5
HallC5×C169 ⋊ C4×C7

Subgroups

subgroupG/H
center, hypercenterC5×C7#10621721
commutator, hypocenterC169C4×C5×C7
FrattiniC13C5×C7×#261
FittingC5×C7×C169C4
socleC5×C7×C13#261
prime radicalC5×C7×D169C2
cosocleD169C2×C5×C7
LCSG ▷ C169
UCSC1 ◁ C5×C7

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5915

Conjugacy classes & character table

1610 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23660, 10);