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C13×C7⋊Dic63 #37524397

order22932
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C7

Aliases

direct productC13×C7⋊Dic63
unambiguous semidirect productC7⋊(C13×Dic63)
unambiguous semidirect productC9⋊(C13×C7⋊Dic7)

Splittings

derived, HallC72×C9 ⋊ C4×C13
HallC72×C9×C13 ⋊ C4
HallC72×C13 ⋊ Dic9
HallC9×C13 ⋊ C7⋊Dic7
SylowC72 ⋊ C13×Dic9
SylowC9 ⋊ C13×C7⋊Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C13C7⋊D63
commutator, hypocenterC72×C9C4×C13
FrattiniC2×C3C13×C3⋊(C7⋊D7)
FittingC2×C72×C9×C13C2
socle, prime radicalC2×C3×C72×C13D3
cosocleC2×C72×C9C2×C13
LCSG ▷ C72×C9
UCSC1 ◁ C2×C13

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22932

Conjugacy classes & character table

5772 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 342);