Finite Group Databasebeta

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C3×C5×Dic3×C41 #20301581

order7380
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C41 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic3×C41
unambiguous semidirect productC3⋊(C3×C4×C5×C41)

Splittings

derivedC3 ⋊ C3×C4×C5×C41
HallC32×C5×C41 ⋊ C4
HallC32×C41 ⋊ C4×C5
HallC32×C5 ⋊ C4×C41
SylowC32 ⋊ C4×C5×C41

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C41D3
commutator, hypocenterC3C3×C4×C5×C41
FrattiniC2C3×C5×D3×C41
Fitting, socleC2×C32×C5×C41C2
LCSG ▷ C3
UCSC1 ◁ C2×C3×C5×C41

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3690 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×Dic3×C41⋊C25, C3×Dic3×C25×C41, C3×C5×Dic3×C41⋊C5, …
maximal normal subgroup ofC3×Dic3×C41⋊C25, C3×Dic3×C25×C41, C3×C5×Dic3×C41⋊C5, …
maximal quotient ofC3×Dic3×C25×C41, C3×C5×C41×Dic15, C3×C52×Dic3×C41, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 59);