Finite Group Databasebeta

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C2×(C7⋊C9)⋊D113 #43249779

order28476
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×(C7⋊C9)⋊D113
unambiguous semidirect product(C2×C7⋊C9)⋊D113
unambiguous semidirect product(C2×C113)⋊(D7⋊C9)
unambiguous semidirect product(C2×D791)⋊C9

Splittings

derived, HallC7×C113 ⋊ C22×C9
HallC7⋊C9×C113 ⋊ C22
HallC2×D791 ⋊ C9
SylowC113 ⋊ C2×D7⋊C9
HallC7⋊C9 ⋊ C2×D113
SylowC7 ⋊ C2×C9×D113

Subgroups

subgroupG/H
center, hypercenterC2×C3ΓL(1,𝔽8)⋊D113
commutator, hypocenterC7×C113C22×C9
FrattiniC3C2×ΓL(1,𝔽8)⋊D113
Fitting, socleC2×C3×C7×C113C2×C3
prime radicalC2×C3×D791C3
cosocleC3×C7×C113C22×C3
LCSG ▷ C7×C113
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14238

Conjugacy classes & character table

1722 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28476, 30);