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Dic21×C97 #22550896

order8148
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C4×C97 · Schur multiplier (H2) = C1

Aliases

direct productDic21×C97
unambiguous semidirect productC3⋊(Dic7×C97)
unambiguous semidirect productC7⋊(Dic3×C97)

Splittings

derived, HallC3×C7 ⋊ C4×C97
HallC3×C7×C97 ⋊ C4
HallC7×C97 ⋊ Dic3
HallC3×C97 ⋊ Dic7
SylowC7 ⋊ Dic3×C97
SylowC3 ⋊ Dic7×C97

Subgroups

subgroupG/H
center, hypercenterC2×C97D21
commutator, hypocenterC3×C7C4×C97
FrattiniC2D21×C97
Fitting, socleC2×C3×C7×C97C2
LCSG ▷ C3×C7
UCSC1 ◁ C2×C97

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2328 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC97×Dic63, C97×C3⋊(ΓL(1,𝔽8)⋊C4), C3⋊#22550904, …
maximal normal subgroup ofC97×C3⋊(ΓL(1,𝔽8)⋊C4), C3⋊#22550904, C3⋊#22550905, …
maximal quotient ofC97×Dic63, C97×C3⋊Dic21, C3×Dic21×C97

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8148, 11);