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C22×C3×C113⋊C7 #23748786

order9492
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC22×C3×C113⋊C7
unambiguous semidirect product(C22×C3×C113)⋊C7

Splittings

Fitting, socle, HallC22×C3×C113 ⋊ C7
derived, SylowC113 ⋊ C22×C3×C7
HallC22×C113 ⋊ C3×C7
HallC3×C113 ⋊ C22×C7

Subgroups

subgroupG/H
center, hypercenterC22×C3C113⋊C7
commutator, cosocle, hypocenterC113C22×C3×C7
FrattiniC1G
Fitting, socleC22×C3×C113C7
LCSG ▷ C113
UCSC1 ◁ C22×C3

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

276 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22⋊C9×C113⋊C7, C22×C9×C113⋊C7, C3×A4×C113⋊C7, …
maximal normal subgroup ofC22⋊C9×C113⋊C7, C22×C9×C113⋊C7, C3×A4×C113⋊C7, …
maximal quotient ofC22×C9×C113⋊C7, C2×C3×D3×C113⋊C7, C22×C32×C113⋊C7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9492, 28);