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C4×C7⋊C9×C127 #44544622

order32004
automorphism?
homologyAbelianization (H1) = C4×C9×C127 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7⋊C9×C127
unambiguous semidirect product(C4×C7)⋊(C9×C127)

Splittings

derived, SylowC7 ⋊ C4×C9×C127
HallC4×C7×C127 ⋊ C9
HallC7×C127 ⋊ C4×C9
HallC4×C7 ⋊ C9×C127

Subgroups

subgroupG/H
center, hypercenterC3×C4×C127ΓL(1,𝔽8)
commutator, hypocenterC7C4×C9×C127
FrattiniC2×C3C2×ΓL(1,𝔽8)×C127
FittingC3×C4×C7×C127C3
socle, prime radicalC2×C3×C7×C127C2×C3
cosocleC2×C3×C7C2×C3×C127
LCSG ▷ C7
UCSC1 ◁ C3×C4×C127

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32004

Conjugacy classes & character table

7620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 4);