Finite Group Databasebeta

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C2×C3×C29×D77 #40999690

order26796
automorphism?
homologyAbelianization (H1) = C22×C3×C29 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C29×D77
unambiguous semidirect product(C2×C11)⋊(C3×D7×C29)

Splittings

Fitting, socleC2×C3×C7×C11×C29 ⋊ C2
derived, HallC7×C11 ⋊ C22×C3×C29
HallC3×C7×C11×C29 ⋊ C22
HallC7×C11×C29 ⋊ C22×C3
HallC3×C11×C29 ⋊ C2×D7
HallC3×C7×C29 ⋊ C2×D11
HallC11×C29 ⋊ C2×C3×D7
HallC3×C7×C11 ⋊ C22×C29
HallC7×C29 ⋊ C2×C3×D11
HallC3×C11 ⋊ C2×D7×C29
HallC3×C7 ⋊ C2×D11×C29
SylowC11 ⋊ C2×C3×D7×C29
SylowC7 ⋊ C2×C3×D11×C29

Subgroups

subgroupG/H
center, hypercenterC2×C3×C29D77
commutator, cosocle, hypocenterC7×C11C22×C3×C29
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C29C2
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C29

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13398

Conjugacy classes & character table

6960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26796, 123);