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C2×C5×C7×D61 #22555431

order8540
isoclinismisoclinic class of D61
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×D61

Splittings

Fitting, socleC2×C5×C7×C61 ⋊ C2
derived, SylowC61 ⋊ C22×C5×C7
HallC5×C7×C61 ⋊ C22
HallC7×C61 ⋊ C22×C5
HallC5×C61 ⋊ C22×C7

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D61
commutator, hypocenterC61C22×C5×C7
FrattiniC1G
Fitting, socleC2×C5×C7×C61C2
LCSG ▷ C61
UCSC1 ◁ C2×C5×C7

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2240 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C7×D61⋊C3, C2×C5×#14579421, C2×C5×#14579420, …
maximal normal subgroup ofC2×C5×C7×D61⋊C3, C2×C5×#14579421, C2×C5×#14579420, …
maximal quotient ofC5×D3×C7×D61, C2×C3×C5×C7×D61, C2×C5×C7×D183

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8540, 46);