Finite Group Databasebeta

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C7×#10625194⋊C3 #29509592

order15540
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×#10625194⋊C3
unambiguous semidirect product#10625194⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C7×C37 ⋊ C3×C4
derived, HallC5×C37 ⋊ C3×C4×C7
HallC7×#10625194 ⋊ C3
HallC5×C7×C37⋊C3 ⋊ C4
HallC7×C37⋊C3 ⋊ Dic5
Hall#10625194 ⋊ C3×C7
HallC5×C37⋊C3 ⋊ C4×C7
HallC7×C37 ⋊ C3×Dic5
HallC37⋊C3 ⋊ C7×Dic5
SylowC37 ⋊ C3×C7×Dic5
HallC5×C7 ⋊ #3866⋊C3
SylowC5 ⋊ C7×#3866⋊C3

Subgroups

subgroupG/H
center, hypercenterC7#10625194⋊C3
commutator, hypocenterC5×C37C3×C4×C7
FrattiniC1G
Fitting, socleC5×C7×C37C3×C4
prime radicalC5×C7×D37⋊C3C2
cosocleC5×D37C2×C3×C7
LCSG ▷ C5×C37
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1295

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15540, 94);