Finite Group Databasebeta

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C2×C7×D97⋊C9 #37567775

order24444
automorphism?
homologyAbelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D97⋊C9
unambiguous semidirect productD97⋊(C2×C7×C9)
unambiguous semidirect product(C2×D97)⋊(C7×C9)
unambiguous semidirect product(C97⋊C9)⋊(C22×C7)
unambiguous semidirect product(C2×C97⋊C9)⋊(C2×C7)

Splittings

derived, SylowC97 ⋊ C22×C7×C9
HallC7×C97⋊C9 ⋊ C22
HallC2×C7×D97 ⋊ C9
HallC97⋊C9 ⋊ C22×C7
HallC7×C97 ⋊ C22×C9
HallC2×D97 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D97⋊C3
commutator, hypocenterC97C22×C7×C9
FrattiniC3C2×C7×D97⋊C3
Fitting, socleC2×C3×C7×C97C2×C3
prime radicalC2×C3×C7×D97C3
cosocleC3×C97C22×C3×C7
LCSG ▷ C97
UCSC1 ◁ C2×C3×C7

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12222

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24444, 38);