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C2×C3×C13×D77 #26046593

order12012
isoclinismisoclinic class of D77
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C13×D77
unambiguous semidirect product(C2×C11)⋊(C3×C13×D7)

Splittings

Fitting, socleC2×C3×C7×C11×C13 ⋊ C2
derived, HallC7×C11 ⋊ C22×C3×C13
HallC3×C7×C11×C13 ⋊ C22
HallC7×C11×C13 ⋊ C22×C3
HallC3×C11×C13 ⋊ C2×D7
HallC3×C7×C13 ⋊ C2×D11
HallC3×C7×C11 ⋊ C22×C13
HallC11×C13 ⋊ C2×C3×D7
HallC7×C13 ⋊ C2×C3×D11
HallC3×C11 ⋊ C2×C13×D7
HallC3×C7 ⋊ C2×C13×D11
SylowC11 ⋊ C2×C3×C13×D7
SylowC7 ⋊ C2×C3×C13×D11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13D77
commutator, cosocle, hypocenterC7×C11C22×C3×C13
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C13C2
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3120 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C13×C11⋊(D7⋊C9), C2×C11⋊#13109900, C2×C11⋊#13109901, …
maximal normal subgroup ofC2×C13×C11⋊(D7⋊C9), C2×C11⋊#13109900, C2×C11⋊#13109901, …
maximal quotient ofC2×C9×C13×D77, C3×D3×C13×D77, C2×C32×C13×D77, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 183);