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C2×#11765917⋊C7 #30630650

order16002
automorphism?
homologyAbelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC2×#11765917⋊C7
unambiguous semidirect product(C2×#11765917)⋊C7

Splittings

derived, SylowC127 ⋊ C2×C7×C9
HallC2×#11765917 ⋊ C7
HallC2×C127⋊C7 ⋊ C9
Hall#11765917 ⋊ C2×C7
HallC127⋊C7 ⋊ C2×C9
HallC2×C127 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3(C127⋊C3)⋊C7
commutator, hypocenterC127C2×C7×C9
FrattiniC3C2×(C127⋊C3)⋊C7
Fitting, socleC2×C3×C127C3×C7
prime radicalC2×C3×C127⋊C7C3
cosocleC3×C127C2×C3×C7
LCSG ▷ C127
UCSC1 ◁ C2×C3

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

162 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#11765917⋊C7, (#11765917⋊C4)⋊C7, C2×(#11765917⋊C2)⋊C7, …
maximal normal subgroup ofC4×#11765917⋊C7, (#11765917⋊C4)⋊C7, C2×(#11765917⋊C2)⋊C7, …
maximal quotient ofC4×#11765917⋊C7, C22×#11765917⋊C7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16002, 7);