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C7×C3⋊D285 #26046219

order11970
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C3

Aliases

direct productC7×C3⋊D285
unambiguous semidirect productC3⋊(C7×D285)
unambiguous semidirect productC5⋊(C7×C3⋊D57)
unambiguous semidirect productC19⋊(C7×C3⋊D15)

Splittings

Fitting, socle, HallC32×C5×C7×C19 ⋊ C2
derived, HallC32×C5×C19 ⋊ C2×C7
HallC32×C7×C19 ⋊ D5
HallC5×C7×C19 ⋊ C3⋊D3
HallC32×C5×C7 ⋊ D19
HallC32×C19 ⋊ C7×D5
HallC7×C19 ⋊ C3⋊D15
HallC5×C19 ⋊ C7×C3⋊D3
HallC32×C7 ⋊ D95
HallC32×C5 ⋊ C7×D19
HallC5×C7 ⋊ C3⋊D57
SylowC19 ⋊ C7×C3⋊D15
SylowC32 ⋊ C7×D95
SylowC5 ⋊ C7×C3⋊D57

Subgroups

subgroupG/H
center, hypercenterC7C3⋊D285
commutator, cosocle, hypocenterC32×C5×C19C2×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C19C2
LCSG ▷ C32×C5×C19
UCSC1 ◁ C7

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3003 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C7×D285, C7×D15×D57, D21⋊D285, …
maximal normal subgroup ofD3×C7×D285, C7×D15×D57, D21⋊D285, …
maximal quotient ofC7×C3⋊Dic285, C2×C7×C3⋊D285

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 148);