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C9×Dic127⋊C7 #44544633

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

Aliases

direct productC9×Dic127⋊C7
unambiguous semidirect product(C9×Dic127)⋊C7

Splittings

derived, SylowC127 ⋊ C4×C7×C9
HallC9×C127⋊C7 ⋊ C4
HallC9×Dic127 ⋊ C7
HallC9×C127 ⋊ C4×C7
HallC127⋊C7 ⋊ C4×C9
HallDic127 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C9D127⋊C7
commutator, hypocenterC127C4×C7×C9
FrattiniC2×C3C3×D127⋊C7
FittingC2×C9×C127C2×C7
socle, cosocleC2×C3×C127C2×C3×C7
prime radicalC2×C3×C127⋊C7C2×C3
LCSG ▷ C127
UCSC1 ◁ C2×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4572

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 15);