Finite Group Databasebeta

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C127×C22⋊(C7⋊C9) #44544684

order32004
automorphism?
homologyAbelianization (H1) = C9×C127 · Schur multiplier (H2) = C2

Aliases

direct productC127×C22⋊(C7⋊C9)
unambiguous semidirect productC22⋊(C7⋊C9×C127)
unambiguous semidirect productC7⋊(C22⋊C9×C127)

Splittings

derived, HallC22×C7 ⋊ C9×C127
HallC22×C7×C127 ⋊ C9
HallC7×C127 ⋊ C22⋊C9
HallC22×C127 ⋊ C7⋊C9
SylowC7 ⋊ C22⋊C9×C127
SylowC22 ⋊ C7⋊C9×C127

Subgroups

subgroupG/H
center, hypercenterC3×C127C22⋊ΓL(1,𝔽8)
commutator, hypocenterC22×C7C9×C127
FrattiniC3C22⋊ΓL(1,𝔽8)×C127
Fitting, socle, prime radicalC22×C3×C7×C127C3
cosocleC22×C3×C7C3×C127
LCSG ▷ C22×C7
UCSC1 ◁ C3×C127

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16002

Conjugacy classes & character table

4572 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 66);