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C4×C7×C112⋊C3 #23778997

order10164
isoclinismisoclinic class of C112⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C11

Aliases

direct productC4×C7×C112⋊C3
unambiguous semidirect product(C4×C112)⋊(C3×C7)

Splittings

Fitting, HallC4×C7×C112 ⋊ C3
derived, SylowC112 ⋊ C3×C4×C7
HallC7×C112 ⋊ C3×C4
HallC4×C112 ⋊ C3×C7

Subgroups

subgroupG/H
center, hypercenterC4×C7C112⋊C3
commutator, hypocenterC112C3×C4×C7
FrattiniC2C2×C7×C112⋊C3
FittingC4×C7×C112C3
socleC2×C7×C112C2×C3
prime radicalC2×C7×C112⋊C3C2
cosocleC2×C112C2×C3×C7
LCSG ▷ C112
UCSC1 ◁ C4×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1204 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×ΓL(1,𝔽8)×C112⋊C3, C7×Dic3×C112⋊C3, C3×C4×C7×C112⋊C3
maximal normal subgroup ofC4×ΓL(1,𝔽8)×C112⋊C3, C3×C4×C7×C112⋊C3
maximal quotient ofC4×C7×C112⋊C9, C7×Dic3×C112⋊C3, C3×C4×C7×C112⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10164, 49);