Finite Group Databasebeta

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C22×C11×ΓL(1,𝔽8)×C37 #46803299

order34188
automorphism?
homologyAbelianization (H1) = C22×C3×C11×C37 · Schur multiplier (H2) = C2

Aliases

direct productC22×C11×ΓL(1,𝔽8)×C37

Splittings

Fitting, socle, HallC22×C7×C11×C37 ⋊ C3
derived, SylowC7 ⋊ C22×C3×C11×C37
HallC7×C11×C37 ⋊ C22×C3
HallC22×C7×C37 ⋊ C3×C11
HallC22×C7×C11 ⋊ C3×C37
HallC7×C37 ⋊ C22×C3×C11
HallC7×C11 ⋊ C22×C3×C37
HallC22×C7 ⋊ C3×C11×C37

Subgroups

subgroupG/H
center, hypercenterC22×C11×C37ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C22×C3×C11×C37
FrattiniC1G
Fitting, socleC22×C7×C11×C37C3
LCSG ▷ C7
UCSC1 ◁ C22×C11×C37

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11396

Conjugacy classes & character table

8140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 171);