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C4×C7×#87704 #26013861

order11172
isoclinismisoclinic class of #87704
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×#87704

Splittings

Fitting, HallC4×C72×C19 ⋊ C3
derivedC7×C19 ⋊ C3×C4×C7
HallC72×C19 ⋊ C3×C4
HallC4×C72 ⋊ C19⋊C3
HallC4×C19 ⋊ C7×ΓL(1,𝔽8)
SylowC72 ⋊ C4×C19⋊C3
SylowC19 ⋊ C4×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC4×C7#87704
commutator, hypocenterC7×C19C3×C4×C7
FrattiniC2C2×C7×#87704
FittingC4×C72×C19C3
socleC2×C72×C19C2×C3
prime radicalC2×C7×#87704C2
cosocleC2×C7×C19C2×C3×C7
LCSG ▷ C7×C19
UCSC1 ◁ C4×C7

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1316 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C7×ΓL(1,𝔽8)×C19⋊C3, C4×ΓL(1,𝔽8)×#87704, C4×#3861⋊(C19⋊C3), …
maximal normal subgroup ofC4×C7×ΓL(1,𝔽8)×C19⋊C3, C4×ΓL(1,𝔽8)×#87704, C4×#3861⋊(C19⋊C3), …
maximal quotient ofC4×C7×#11924776, C7×Dic3×#87704, C3×C4×C7×#87704

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11172, 123);