Finite Group Databasebeta

← Prev (#19129675) Next (#19129677) →

C7×Dic195 #19129676

order5460
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic195
unambiguous semidirect productC3⋊(C7×Dic65)

Splittings

derived, HallC3×C5×C13 ⋊ C4×C7
HallC3×C5×C7×C13 ⋊ C4
HallC5×C7×C13 ⋊ Dic3
HallC3×C7×C13 ⋊ Dic5
HallC3×C5×C7 ⋊ Dic13
HallC7×C13 ⋊ Dic15
HallC5×C13 ⋊ C7×Dic3
HallC3×C13 ⋊ C7×Dic5
HallC5×C7 ⋊ Dic39
HallC3×C7 ⋊ Dic65
HallC3×C5 ⋊ C7×Dic13
SylowC13 ⋊ C7×Dic15
SylowC5 ⋊ C7×Dic39
SylowC3 ⋊ C7×Dic65

Subgroups

subgroupG/H
center, hypercenterC2×C7D195
commutator, hypocenterC3×C5×C13C4×C7
FrattiniC2C7×D195
Fitting, socleC2×C3×C5×C7×C13C2
LCSG ▷ C3×C5×C13
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1386 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×Dic585, C7×C3⋊(Dic65⋊C3), C3⋊#19129697, …
maximal normal subgroup ofC7×C3⋊(Dic65⋊C3), C3⋊#19129697, C3⋊#19129698, …
maximal quotient ofC7×Dic585, C3×C7×Dic195, C7×C3⋊Dic195, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 18);