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C4×C7×#11765919 #44544722

order32004
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×#11765919

Splittings

Fitting, HallC4×C7×C127 ⋊ C9
derived, SylowC127 ⋊ C4×C7×C9
HallC7×C127 ⋊ C4×C9
HallC4×C127 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC4×C7#11765919
commutator, hypocenterC127C4×C7×C9
FrattiniC2C2×C7×#11765919
FittingC4×C7×C127C9
socleC2×C7×C127C2×C9
prime radicalC2×C7×C127⋊C3C2×C3
cosocleC2×C127⋊C3C2×C3×C7
LCSG ▷ C127
UCSC1 ◁ C4×C7

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3556

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 104);