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C67×Dic21 #19150583

order5628
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C4×C67 · Schur multiplier (H2) = C1

Aliases

direct productC67×Dic21
unambiguous semidirect productC3⋊(Dic7×C67)
unambiguous semidirect productC7⋊(Dic3×C67)

Splittings

derived, HallC3×C7 ⋊ C4×C67
HallC3×C7×C67 ⋊ C4
HallC7×C67 ⋊ Dic3
HallC3×C67 ⋊ Dic7
SylowC7 ⋊ Dic3×C67
SylowC3 ⋊ Dic7×C67

Subgroups

subgroupG/H
center, hypercenterC2×C67D21
commutator, hypocenterC3×C7C4×C67
FrattiniC2D21×C67
Fitting, socleC2×C3×C7×C67C2
LCSG ▷ C3×C7
UCSC1 ◁ C2×C67

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1608 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC67×Dic63, C67×C3⋊(ΓL(1,𝔽8)⋊C4), C3⋊#19150592, …
maximal normal subgroup ofC67×C3⋊(ΓL(1,𝔽8)⋊C4), C3⋊#19150592, C3⋊#19150591, …
maximal quotient ofC67×Dic63, C3×C67×Dic21, C67×C3⋊Dic21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5628, 11);