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C4×C13×C49⋊C9 #37524070

order22932
automorphism?
homologyAbelianization (H1) = C4×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC4×C13×C49⋊C9
unambiguous semidirect product(C4×C49)⋊(C9×C13)

Splittings

derived, SylowC49 ⋊ C4×C9×C13
HallC4×C13×C49 ⋊ C9
HallC13×C49 ⋊ C4×C9
HallC4×C49 ⋊ C9×C13

Subgroups

subgroupG/H
center, hypercenterC3×C4×C13C49⋊C3
commutator, hypocenterC49C4×C9×C13
FrattiniC2×C3×C7C2×C13×ΓL(1,𝔽8)
FittingC3×C4×C13×C49C3
socle, prime radicalC2×C3×C7×C13C2×ΓL(1,𝔽8)
cosocleC2×C3×C49C2×C3×C13
LCSG ▷ C49
UCSC1 ◁ C3×C4×C13

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22932

Conjugacy classes & character table

2964 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 15);