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C4×C7×C197⋊C7 #50311014

order38612
automorphism?
homologyAbelianization (H1) = C4×C72 · Schur multiplier (H2) = C7

Aliases

direct productC4×C7×C197⋊C7
unambiguous semidirect product(C4×C197)⋊C72
unambiguous semidirect product(C4×C7×C197)⋊C7

Splittings

FittingC4×C7×C197 ⋊ C7
derived, SylowC197 ⋊ C4×C72
HallC4×C197 ⋊ C72

Subgroups

subgroupG/H
center, hypercenterC4×C7C197⋊C7
commutator, hypocenterC197C4×C72
FrattiniC2C2×C7×C197⋊C7
FittingC4×C7×C197C7
socleC2×C7×C197C2×C7
prime radicalC2×C7×C197⋊C7C2
cosocleC2×C197C2×C72
LCSG ▷ C197
UCSC1 ◁ C4×C7

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

980 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38612, 23);