Finite Group Databasebeta

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C2×C112×D7⋊C9 #44478939

order30492
automorphism?
homologyAbelianization (H1) = C22×C9×C112 · Schur multiplier (H2) = C2×C11

Aliases

direct productC2×C112×D7⋊C9
unambiguous semidirect productD7⋊(C2×C9×C112)
unambiguous semidirect product(C2×D7)⋊(C9×C112)
unambiguous semidirect product(C7⋊C9)⋊(C22×C112)
unambiguous semidirect product(C2×C7⋊C9)⋊(C2×C112)
unambiguous semidirect product(C2×C11×D7)⋊(C9×C11)

Splittings

derived, SylowC7 ⋊ C22×C9×C112
HallC112×C7⋊C9 ⋊ C22
HallC2×C112×D7 ⋊ C9
HallC7×C112 ⋊ C22×C9
HallC7⋊C9 ⋊ C22×C112
HallC2×D7 ⋊ C9×C112

Subgroups

subgroupG/H
center, hypercenterC2×C3×C112AGL(1,𝔽7)
commutator, hypocenterC7C22×C9×C112
FrattiniC3C2×C112×AGL(1,𝔽7)
Fitting, socleC2×C3×C7×C112C2×C3
prime radicalC2×C3×C112×D7C3
cosocleC3×C7C22×C3×C112
LCSG ▷ C7
UCSC1 ◁ C2×C3×C112

420 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15246

Conjugacy classes & character table

5082 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 162);