Finite Group Databasebeta

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C7×C9×#87604 #37567787

order24444
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×#87604

Splittings

Fitting, HallC7×C9×C97 ⋊ C4
derived, SylowC97 ⋊ C4×C7×C9
HallC9×C97 ⋊ C4×C7
HallC7×C97 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC7×C9#87604
commutator, hypocenterC97C4×C7×C9
FrattiniC3C3×C7×#87604
FittingC7×C9×C97C4
socleC3×C7×C97C3×C4
prime radicalC3×C7×D97C2×C3
cosocleC3×D97C2×C3×C7
LCSG ▷ C97
UCSC1 ◁ C7×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6111

Conjugacy classes & character table

1764 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24444, 50);