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C7×D795 #26013281

order11130
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D795
unambiguous semidirect productC3⋊(C7×D265)
unambiguous semidirect productC5⋊(C7×D159)
unambiguous semidirect productC53⋊(C7×D15)

Splittings

Fitting, socle, HallC3×C5×C7×C53 ⋊ C2
derived, HallC3×C5×C53 ⋊ C2×C7
HallC5×C7×C53 ⋊ D3
HallC3×C7×C53 ⋊ D5
HallC7×C53 ⋊ D15
HallC5×C53 ⋊ D3×C7
HallC3×C53 ⋊ C7×D5
HallC3×C5×C7 ⋊ D53
SylowC53 ⋊ C7×D15
HallC5×C7 ⋊ D159
HallC3×C7 ⋊ D265
HallC3×C5 ⋊ C7×D53
SylowC5 ⋊ C7×D159
SylowC3 ⋊ C7×D265

Subgroups

subgroupG/H
center, hypercenterC7D795
commutator, cosocle, hypocenterC3×C5×C53C2×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C53C2
LCSG ▷ C3×C5×C53
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2793 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×D15×D53, D7×D795, D371⋊D15, …
maximal normal subgroup ofC7×D15×D53, D7×D795, D371⋊D15, …
maximal quotient ofC7×Dic795, C2×C7×D795, C7×D2385, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11130, 15);