Finite Group Databasebeta

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C3×C5×C7⋊#3866 #29509653

order15540
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C7⋊#3866

Splittings

Fitting, socle, HallC3×C5×C7×C37 ⋊ C4
derived, HallC7×C37 ⋊ C3×C4×C5
HallC5×C7×C37 ⋊ C3×C4
HallC3×C7×C37 ⋊ C4×C5
HallC3×C5×C37 ⋊ Dic7
HallC5×C37 ⋊ C3×Dic7
HallC3×C37 ⋊ C5×Dic7
HallC3×C5×C7 ⋊ #3866
SylowC37 ⋊ C3×C5×Dic7
HallC5×C7 ⋊ C3×#3866
HallC3×C7 ⋊ C5×#3866
SylowC7 ⋊ C3×C5×#3866

Subgroups

subgroupG/H
center, hypercenterC3×C5C7⋊#3866
commutator, hypocenterC7×C37C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C37C4
prime radicalC3×C5×C7×D37C2
cosocleC7×D37C2×C3×C5
LCSG ▷ C7×C37
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3885

Conjugacy classes & character table

1095 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15540, 155);