Finite Group Databasebeta

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C7×C9×#92150 #44478951

order30492
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C11

Aliases

direct productC7×C9×#92150

Splittings

Fitting, HallC7×C9×C112 ⋊ C4
derived, SylowC112 ⋊ C4×C7×C9
HallC9×C112 ⋊ C4×C7
HallC7×C112 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC7×C9#92150
commutator, hypocenterC112C4×C7×C9
FrattiniC3C3×C7×#92150
FittingC7×C9×C112C4
socleC3×C7×C112C3×C4
prime radicalC3×C7×C11⋊D11C2×C3
cosocleC3×C11⋊D11C2×C3×C7
LCSG ▷ C112
UCSC1 ◁ C7×C9

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1386

Conjugacy classes & character table

2142 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 174);