Finite Group Databasebeta

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C2×C3×C11×D7×C29 #40999688

order26796
automorphism?
homologyAbelianization (H1) = C22×C3×C11×C29 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C11×D7×C29

Splittings

Fitting, socleC2×C3×C7×C11×C29 ⋊ C2
derived, SylowC7 ⋊ C22×C3×C11×C29
HallC3×C7×C11×C29 ⋊ C22
HallC7×C11×C29 ⋊ C22×C3
HallC3×C7×C29 ⋊ C22×C11
HallC3×C7×C11 ⋊ C22×C29
HallC7×C29 ⋊ C22×C3×C11
HallC7×C11 ⋊ C22×C3×C29
HallC3×C7 ⋊ C22×C11×C29

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11×C29D7
commutator, cosocle, hypocenterC7C22×C3×C11×C29
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C29C2
LCSG ▷ C7
UCSC1 ◁ C2×C3×C11×C29

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13398

Conjugacy classes & character table

9570 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26796, 121);