Finite Group Databasebeta

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C5×C3⋊(C5⋊(C7⋊D7)) #20301329

order7350
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C7

Aliases

direct productC5×C3⋊(C5⋊(C7⋊D7))
unambiguous semidirect productC3⋊(C5×C5⋊(C7⋊D7))
unambiguous semidirect productC5⋊(C5×C3⋊(C7⋊D7))
unambiguous semidirect productC7⋊(C5×D105)

Splittings

Fitting, socle, HallC3×C52×C72 ⋊ C2
derivedC3×C5×C72 ⋊ C2×C5
HallC52×C72 ⋊ D3
HallC3×C72 ⋊ C5×D5
HallC3×C52 ⋊ C7⋊D7
SylowC72 ⋊ C5×D15
SylowC52 ⋊ C3⋊(C7⋊D7)
SylowC3 ⋊ C5×C5⋊(C7⋊D7)

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C5⋊(C7⋊D7))
commutator, hypocenterC3×C5×C72C2×C5
FrattiniC1G
Fitting, socleC3×C52×C72C2
LCSG ▷ C3×C5×C72
UCSC1 ◁ C5

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1845 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D15×C7⋊D7, C5×D7×D105, C5×D5×C3⋊(C7⋊D7), …
maximal normal subgroup ofC5×D15×C7⋊D7, C5×D7×D105, C5×D5×C3⋊(C7⋊D7), …
maximal quotient ofC5×C3⋊(C7⋊Dic35), C2×C5×C3⋊(C5⋊(C7⋊D7)), C5×C5⋊(C7⋊D63), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7350, 152);