Finite Group Databasebeta

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Dic3×C13×C61 #23748900

order9516
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C4×C13×C61 · Schur multiplier (H2) = C1

Aliases

direct productDic3×C13×C61
unambiguous semidirect productC3⋊(C4×C13×C61)

Splittings

derived, SylowC3 ⋊ C4×C13×C61
HallC3×C13×C61 ⋊ C4
HallC3×C61 ⋊ C4×C13
HallC3×C13 ⋊ C4×C61

Subgroups

subgroupG/H
center, hypercenterC2×C13×C61D3
commutator, hypocenterC3C4×C13×C61
FrattiniC2D3×C13×C61
Fitting, socle, prime radicalC2×C3×C13×C61C2
cosocleC2×C3C2×C13×C61
LCSG ▷ C3
UCSC1 ◁ C2×C13×C61

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4758 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC13×Dic9×C61, Dic3×C13×C61⋊C3, Dic3×C13⋊C3×C61, …
maximal normal subgroup ofDic3×C13×C61⋊C3, Dic3×C13⋊C3×C61, Dic3×#14558651, …
maximal quotient ofC13×Dic9×C61, C13×C3⋊Dic3×C61, C3×Dic3×C13×C61

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9516, 9);