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C4×C7⋊C9×C97 #37567740

order24444
automorphism?
homologyAbelianization (H1) = C4×C9×C97 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7⋊C9×C97
unambiguous semidirect product(C4×C7)⋊(C9×C97)

Splittings

derived, SylowC7 ⋊ C4×C9×C97
HallC4×C7×C97 ⋊ C9
HallC7×C97 ⋊ C4×C9
HallC4×C7 ⋊ C9×C97

Subgroups

subgroupG/H
center, hypercenterC3×C4×C97ΓL(1,𝔽8)
commutator, hypocenterC7C4×C9×C97
FrattiniC2×C3C2×ΓL(1,𝔽8)×C97
FittingC3×C4×C7×C97C3
socle, prime radicalC2×C3×C7×C97C2×C3
cosocleC2×C3×C7C2×C3×C97
LCSG ▷ C7
UCSC1 ◁ C3×C4×C97

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24444

Conjugacy classes & character table

5820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24444, 3);