Finite Group Databasebeta

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C7×C22⋊(C112⋊C9) #44478979

order30492
automorphism?
homologyAbelianization (H1) = C7×C9 · Schur multiplier (H2) = C2×C11

Aliases

direct productC7×C22⋊(C112⋊C9)
unambiguous semidirect productC22⋊(C7×C112⋊C9)
unambiguous semidirect productC112⋊(C7×C22⋊C9)

Splittings

derived, HallC22×C112 ⋊ C7×C9
HallC22×C7×C112 ⋊ C9
HallC7×C112 ⋊ C22⋊C9
SylowC112 ⋊ C7×C22⋊C9
HallC22×C7 ⋊ C112⋊C9
SylowC22 ⋊ C7×C112⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C7C22⋊(C112⋊C3)
commutator, hypocenterC22×C112C7×C9
FrattiniC3C7×C22⋊(C112⋊C3)
Fitting, socle, prime radicalC22×C3×C7×C112C3
cosocleC22×C3×C112C3×C7
LCSG ▷ C22×C112
UCSC1 ◁ C3×C7

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1386

Conjugacy classes & character table

3444 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 202);