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C5×C3⋊D357 #24924231

order10710
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×C3⋊D357
unambiguous semidirect productC3⋊(C5×D357)
unambiguous semidirect productC7⋊(C5×C3⋊D51)
unambiguous semidirect productC17⋊(C5×C3⋊D21)

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C2
derived, HallC32×C7×C17 ⋊ C2×C5
HallC32×C5×C17 ⋊ D7
HallC5×C7×C17 ⋊ C3⋊D3
HallC32×C5×C7 ⋊ D17
HallC32×C17 ⋊ C5×D7
HallC7×C17 ⋊ C5×C3⋊D3
HallC5×C17 ⋊ C3⋊D21
HallC32×C7 ⋊ C5×D17
HallC32×C5 ⋊ D119
HallC5×C7 ⋊ C3⋊D51
SylowC17 ⋊ C5×C3⋊D21
SylowC32 ⋊ C5×D119
SylowC7 ⋊ C5×C3⋊D51

Subgroups

subgroupG/H
center, hypercenterC5C3⋊D357
commutator, cosocle, hypocenterC32×C7×C17C2×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C17C2
LCSG ▷ C32×C7×C17
UCSC1 ◁ C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2685 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D3×D357, C5×D21×D51, D15⋊D357, …
maximal normal subgroup ofC5×D3×D357, C5×D21×D51, D15⋊D357, …
maximal quotient ofC5×C3⋊Dic357, C2×C5×C3⋊D357

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 46);