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C7×Dic693 #34084652

order19404
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic693
unambiguous semidirect productC7⋊(C7×Dic99)
unambiguous semidirect productC9⋊(C7×Dic77)
unambiguous semidirect productC11⋊(C7×Dic63)

Splittings

derivedC7×C9×C11 ⋊ C4×C7
HallC72×C9×C11 ⋊ C4
HallC72×C11 ⋊ Dic9
HallC72×C9 ⋊ Dic11
HallC9×C11 ⋊ C7×Dic7
SylowC72 ⋊ Dic99
SylowC11 ⋊ C7×Dic63
SylowC9 ⋊ C7×Dic77

Subgroups

subgroupG/H
center, hypercenterC2×C7D693
commutator, hypocenterC7×C9×C11C4×C7
FrattiniC2×C3C7×D231
FittingC2×C72×C9×C11C2
socle, prime radicalC2×C3×C72×C11D3
cosocleC2×C7×C9×C11C2×C7
LCSG ▷ C7×C9×C11
UCSC1 ◁ C2×C7

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Conjugacy classes & character table

4872 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19404, 143);