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C5×C3⋊D3×D41 #20301628

order7380
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC5×C3⋊D3×D41

Splittings

Fitting, socle, HallC32×C5×C41 ⋊ C22
derived, HallC32×C41 ⋊ C22×C5
HallC5×C41 ⋊ C2×C3⋊D3
HallC32×C5 ⋊ C2×D41
SylowC41 ⋊ C2×C5×C3⋊D3
SylowC32 ⋊ C2×C5×D41

Subgroups

subgroupG/H
center, hypercenterC5C3⋊D3×D41
commutator, hypocenterC32×C41C22×C5
FrattiniC1G
Fitting, socleC32×C5×C41C22
LCSG ▷ C32×C41
UCSC1 ◁ C5

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3⋊D3×D41⋊C25, C3⋊D3×C25×D41, C5×C3⋊D3×D41⋊C5, …
maximal normal subgroup ofC3⋊D3×D41⋊C25, C3⋊D3×C25×D41, C5×C3⋊D3×D41⋊C5, …
maximal quotient ofC3⋊D3×C25×D41, C52×C3⋊D3×D41, C5×D41×C3⋊D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 106);