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C22×#11765917⋊C7 #44544652

order32004
automorphism?
homologyAbelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC22×#11765917⋊C7
unambiguous semidirect product(C22×#11765917)⋊C7

Splittings

derived, SylowC127 ⋊ C22×C7×C9
HallC22×#11765917 ⋊ C7
HallC22×C127⋊C7 ⋊ C9
Hall#11765917 ⋊ C22×C7
HallC127⋊C7 ⋊ C22×C9
HallC22×C127 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC22×C3(C127⋊C3)⋊C7
commutator, hypocenterC127C22×C7×C9
FrattiniC3C22×(C127⋊C3)⋊C7
Fitting, socleC22×C3×C127C3×C7
prime radicalC22×C3×C127⋊C7C3
cosocleC3×C127C22×C3×C7
LCSG ▷ C127
UCSC1 ◁ C22×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4572

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 34);