Finite Group Databasebeta

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C3×C5×C13×D21 #22551297

order8190
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C13×D21
unambiguous semidirect productC3⋊(C3×C5×C13×D7)

Splittings

Fitting, socle, HallC32×C5×C7×C13 ⋊ C2
derivedC3×C7 ⋊ C2×C3×C5×C13
HallC32×C7×C13 ⋊ C2×C5
HallC32×C5×C13 ⋊ D7
HallC5×C7×C13 ⋊ C3×D3
HallC32×C5×C7 ⋊ C2×C13
HallC32×C13 ⋊ C5×D7
HallC7×C13 ⋊ C3×C5×D3
HallC32×C7 ⋊ C2×C5×C13
HallC32×C5 ⋊ C13×D7
HallC5×C7 ⋊ C3×D3×C13
SylowC32 ⋊ C5×C13×D7
SylowC7 ⋊ C3×C5×D3×C13

Subgroups

subgroupG/H
center, hypercenterC3×C5×C13D21
commutator, hypocenterC3×C7C2×C3×C5×C13
FrattiniC1G
Fitting, socleC32×C5×C7×C13C2
LCSG ▷ C3×C7
UCSC1 ◁ C3×C5×C13

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2340 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×D13×D21, C3×C5×D3×C13×D7, C3×C5×D21⋊D13, …
maximal normal subgroup ofC3×C5×D13×D21, C3×C5×D3×C13×D7, C3×C5×D21⋊D13, …
maximal quotient ofC3×C5×C13×Dic21, C2×C3×C5×C13×D21

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8190, 131);